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Base field Conductor norm Rank* Torsion order CM discriminant
Base field degree/signature Bad \(p\) $\Q$-curves Torsion structure CM
Analytic order of Ш* Cyclic isogeny degree Isogeny class size Reduction Galois image
j-invariant Regulator* Curves per isogeny class Isogeny class degree Nonmax$\ \ell$
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Results (12 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
16.1-a1 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( 5699182696 a^{3} - 4361830336 a^{2} - 19458081104 a + 14892491272 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - 2 a\) , \( a^{2} - 2\) , \( a^{3} + 4 a^{2} - 4 a - 5\) , \( 6 a^{3} + 4 a^{2} - 18 a - 14\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(a^{3}+4a^{2}-4a-5\right){x}+6a^{3}+4a^{2}-18a-14$
16.1-a2 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( -5699182696 a^{3} - 4361830336 a^{2} + 19458081104 a + 14892491272 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + 3 a\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 2 a - 1\) , \( -4 a^{3} + 5 a^{2} + 15 a - 13\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(2a-1\right){x}-4a^{3}+5a^{2}+15a-13$
16.1-a3 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( 2360533016 a^{3} + 4361830336 a^{2} - 1382416352 a - 2554830072 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 4 a^{3} - 2 a^{2} - 14 a + 3\) , \( 4 a^{3} - 6 a^{2} - 9 a + 9\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(4a^{3}-2a^{2}-14a+3\right){x}+4a^{3}-6a^{2}-9a+9$
16.1-a4 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( -2360533016 a^{3} + 4361830336 a^{2} + 1382416352 a - 2554830072 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{2} - 2\) , \( -5 a^{3} - 2 a^{2} + 16 a + 7\) , \( -6 a^{3} - 9 a^{2} + 14 a + 18\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-5a^{3}-2a^{2}+16a+7\right){x}-6a^{3}-9a^{2}+14a+18$
16.1-a5 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( -10561278147056904530419721864 a^{3} - 8083252342956303105729121856 a^{2} + 36058459085676274419182662496 a + 27597949777405506664334735112 \) \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 2 a\) , \( -394 a^{3} + 255 a^{2} + 1292 a - 1002\) , \( 5759 a^{3} - 4221 a^{2} - 19434 a + 14903\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-394a^{3}+255a^{2}+1292a-1002\right){x}+5759a^{3}-4221a^{2}-19434a+14903$
16.1-a6 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( 10561278147056904530419721864 a^{3} - 8083252342956303105729121856 a^{2} - 36058459085676274419182662496 a + 27597949777405506664334735112 \) \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a\) , \( 394 a^{3} + 255 a^{2} - 1294 a - 1002\) , \( -5759 a^{3} - 4221 a^{2} + 19434 a + 14903\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(394a^{3}+255a^{2}-1294a-1002\right){x}-5759a^{3}-4221a^{2}+19434a+14903$
16.1-a7 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( -4374624644505560827923496904 a^{3} + 8083252342956303105729121856 a^{2} + 2562595786459777953350768848 a - 4735059594419705758581752312 \) \( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a^{3} - 2 a\) , \( -111 a^{3} - 255 a^{2} - 62 a + 18\) , \( 2157 a^{3} + 4220 a^{2} - 712 a - 1979\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(-111a^{3}-255a^{2}-62a+18\right){x}+2157a^{3}+4220a^{2}-712a-1979$
16.1-a8 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $154.9911952$ 0.856213478 \( 4374624644505560827923496904 a^{3} + 8083252342956303105729121856 a^{2} - 2562595786459777953350768848 a - 4735059594419705758581752312 \) \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 2 a + 3\) , \( a^{3} - 2 a\) , \( 111 a^{3} - 255 a^{2} + 60 a + 18\) , \( -2157 a^{3} + 4220 a^{2} + 712 a - 1979\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+2a+3\right){x}^{2}+\left(111a^{3}-255a^{2}+60a+18\right){x}-2157a^{3}+4220a^{2}+712a-1979$
16.1-a9 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $619.9647811$ 0.856213478 \( -75602392581248 a^{2} + 258122728722624 \) \( \bigl[a^{3} - 2 a\) , \( -a^{3} + 4 a + 1\) , \( 0\) , \( 409 a^{3} - 798 a^{2} - 82 a + 293\) , \( -11769 a^{3} + 22208 a^{2} + 5596 a - 11916\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(409a^{3}-798a^{2}-82a+293\right){x}-11769a^{3}+22208a^{2}+5596a-11916$
16.1-a10 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $619.9647811$ 0.856213478 \( 55168 a^{2} - 30528 \) \( \bigl[a^{3} - 2 a\) , \( a + 1\) , \( a^{3} - 2 a\) , \( -4 a^{3} - 11 a^{2} + 4 a + 6\) , \( -20 a^{3} - 43 a^{2} + 12 a + 25\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a^{3}-11a^{2}+4a+6\right){x}-20a^{3}-43a^{2}+12a+25$
16.1-a11 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $619.9647811$ 0.856213478 \( -55168 a^{2} + 190144 \) \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 0\) , \( 5 a^{3} - 8 a^{2} - 6 a + 7\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(5a^{3}-8a^{2}-6a+7\right){x}$
16.1-a12 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $619.9647811$ 0.856213478 \( 75602392581248 a^{2} - 44286841602368 \) \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 0\) , \( 1845 a^{3} - 3428 a^{2} - 1046 a + 1967\) , \( -98956 a^{3} + 182892 a^{2} + 57892 a - 107052\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(1845a^{3}-3428a^{2}-1046a+1967\right){x}-98956a^{3}+182892a^{2}+57892a-107052$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.