↑

Learn more

Refine search

Base field Base char. Dimension $p$-rank Initial coefficients
Simple Geom. simple Primitive Princ. polarizable Jacobian
Slopes Points on variety Points on curve Simple factors
Newton elevation # Jacobians # Hyp. Jacobians # twists Max twist degree
Angle rank Angle corank End. degree $p$-corank (Geom.) Sq.free
Use Geometric decomposition in the following inputs
Dim 1 factors Dim 2 factors Dim 3 factors Dim 4 factors Dim 5 factors
(distinct) (distinct) (distinct) Number field Galois group
Sort order Select

Results (1-50 of 135930 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.5.ae $1$ $\F_{5}$ $1 - 4 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.5.ad $1$ $\F_{5}$ $1 - 3 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.5.ac $1$ $\F_{5}$ $1 - 2 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.5.ab $1$ $\F_{5}$ $1 - x + 5 x^{2}$ $1$ \(\Q(\sqrt{-19}) \) $C_2$ simple
1.5.a $1$ $\F_{5}$ $1 + 5 x^{2}$ $0$ \(\Q(\sqrt{-5}) \) $C_2$ simple
1.5.b $1$ $\F_{5}$ $1 + x + 5 x^{2}$ $1$ \(\Q(\sqrt{-19}) \) $C_2$ simple
1.5.c $1$ $\F_{5}$ $1 + 2 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.5.d $1$ $\F_{5}$ $1 + 3 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.5.e $1$ $\F_{5}$ $1 + 4 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
2.5.ai_ba $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.5.ae 2
2.5.ah_w $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.5.ae $\times$ 1.5.ad
2.5.ag_r $2$ $\F_{5}$ $1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4}$ $2$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.5.ag_s $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.5.ae $\times$ 1.5.ac
2.5.ag_t $2$ $\F_{5}$ $( 1 - 3 x + 5 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.5.ad 2
2.5.af_n $2$ $\F_{5}$ $1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4}$ $2$ 4.0.4901.1 $D_{4}$ simple
2.5.af_o $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )( 1 - x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.5.ae $\times$ 1.5.ab
2.5.af_p $2$ $\F_{5}$ $1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4}$ $0$ \(\Q(\zeta_{5})\) $C_4$ simple
2.5.af_q $2$ $\F_{5}$ $( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.5.ad $\times$ 1.5.ac
2.5.ae_i $2$ $\F_{5}$ $1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4}$ $2$ \(\Q(i, \sqrt{6})\) $C_2^2$ simple
2.5.ae_j $2$ $\F_{5}$ $1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4}$ $2$ 4.0.1025.1 $D_{4}$ simple
2.5.ae_k $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )( 1 + 5 x^{2} )$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.5.ae $\times$ 1.5.a
2.5.ae_l $2$ $\F_{5}$ $1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4}$ $2$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.5.ae_m $2$ $\F_{5}$ $1 - 4 x + 12 x^{2} - 20 x^{3} + 25 x^{4}$ $2$ 4.0.10496.2 $D_{4}$ simple
2.5.ae_n $2$ $\F_{5}$ $( 1 - 3 x + 5 x^{2} )( 1 - x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.5.ad $\times$ 1.5.ab
2.5.ae_o $2$ $\F_{5}$ $( 1 - 2 x + 5 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.5.ac 2
2.5.ad_e $2$ $\F_{5}$ $1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-11})\) $C_2^2$ simple
2.5.ad_f $2$ $\F_{5}$ $1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4}$ $1$ 4.0.37845.1 $D_{4}$ simple
2.5.ad_g $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )( 1 + x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.5.ae $\times$ 1.5.b
2.5.ad_h $2$ $\F_{5}$ $1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4}$ $2$ 4.0.48069.2 $D_{4}$ simple
2.5.ad_i $2$ $\F_{5}$ $1 - 3 x + 8 x^{2} - 15 x^{3} + 25 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{17})\) $C_2^2$ simple
2.5.ad_j $2$ $\F_{5}$ $1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4}$ $2$ 4.0.30589.1 $D_{4}$ simple
2.5.ad_k $2$ $\F_{5}$ $( 1 - 3 x + 5 x^{2} )( 1 + 5 x^{2} )$ $1$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.5.ad $\times$ 1.5.a
2.5.ad_l $2$ $\F_{5}$ $1 - 3 x + 11 x^{2} - 15 x^{3} + 25 x^{4}$ $2$ 4.0.6525.1 $D_{4}$ simple
2.5.ad_m $2$ $\F_{5}$ $( 1 - 2 x + 5 x^{2} )( 1 - x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.5.ac $\times$ 1.5.ab
2.5.ac_ab $2$ $\F_{5}$ $1 - 2 x - x^{2} - 10 x^{3} + 25 x^{4}$ $2$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.5.ac_a $2$ $\F_{5}$ $1 - 2 x - 10 x^{3} + 25 x^{4}$ $1$ 4.0.38720.3 $D_{4}$ simple
2.5.ac_b $2$ $\F_{5}$ $1 - 2 x + x^{2} - 10 x^{3} + 25 x^{4}$ $2$ 4.0.65600.5 $D_{4}$ simple
2.5.ac_c $2$ $\F_{5}$ $( 1 - 4 x + 5 x^{2} )( 1 + 2 x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.5.ae $\times$ 1.5.c
2.5.ac_d $2$ $\F_{5}$ $1 - 2 x + 3 x^{2} - 10 x^{3} + 25 x^{4}$ $2$ 4.0.5696.1 $D_{4}$ simple
2.5.ac_e $2$ $\F_{5}$ $1 - 2 x + 4 x^{2} - 10 x^{3} + 25 x^{4}$ $2$ 4.0.90944.1 $D_{4}$ simple
2.5.ac_f $2$ $\F_{5}$ $1 - 2 x + 5 x^{2} - 10 x^{3} + 25 x^{4}$ $1$ 4.0.83520.4 $D_{4}$ simple
2.5.ac_g $2$ $\F_{5}$ $1 - 2 x + 6 x^{2} - 10 x^{3} + 25 x^{4}$ $2$ 4.0.4400.1 $D_{4}$ simple
2.5.ac_h $2$ $\F_{5}$ $( 1 - 3 x + 5 x^{2} )( 1 + x + 5 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.5.ad $\times$ 1.5.b
2.5.ac_i $2$ $\F_{5}$ $1 - 2 x + 8 x^{2} - 10 x^{3} + 25 x^{4}$ $2$ 4.0.35136.1 $D_{4}$ simple
2.5.ac_j $2$ $\F_{5}$ $1 - 2 x + 9 x^{2} - 10 x^{3} + 25 x^{4}$ $2$ 4.0.17984.1 $D_{4}$ simple
2.5.ac_k $2$ $\F_{5}$ $( 1 - 2 x + 5 x^{2} )( 1 + 5 x^{2} )$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.5.ac $\times$ 1.5.a
2.5.ac_l $2$ $\F_{5}$ $( 1 - x + 5 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-19}) \) $C_2$ 1.5.ab 2
2.5.ab_af $2$ $\F_{5}$ $1 - x - 5 x^{2} - 5 x^{3} + 25 x^{4}$ $1$ 4.0.18605.1 $D_{4}$ simple
2.5.ab_ae $2$ $\F_{5}$ $1 - x - 4 x^{2} - 5 x^{3} + 25 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-19})\) $C_2^2$ simple
2.5.ab_ad $2$ $\F_{5}$ $1 - x - 3 x^{2} - 5 x^{3} + 25 x^{4}$ $2$ 4.0.81461.1 $D_{4}$ simple
Next   displayed columns for results