Label |
Dimension |
Base field |
Base char. |
L-polynomial |
$p$-rank |
$p$-rank deficit |
points on curve |
points on variety |
Isogeny factors |
2.2.ae_i |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 - 2 x + 2 x^{2} )^{2}$ |
$0$ |
$2$ |
$-1$ |
$1$ |
1.2.ac 2 |
2.2.ac_c |
$2$ |
$\F_{2}$ |
$2$ |
$1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4}$ |
$0$ |
$2$ |
$1$ |
$1$ |
simple |
2.2.ac_e |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )$ |
$0$ |
$2$ |
$1$ |
$3$ |
1.2.ac $\times$ 1.2.a |
2.2.a_ae |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 - 2 x^{2} )^{2}$ |
$0$ |
$2$ |
$3$ |
$1$ |
simple |
2.2.a_ac |
$2$ |
$\F_{2}$ |
$2$ |
$1 - 2 x^{2} + 4 x^{4}$ |
$0$ |
$2$ |
$3$ |
$3$ |
simple |
2.2.a_a |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ |
$0$ |
$2$ |
$3$ |
$5$ |
1.2.ac $\times$ 1.2.c |
2.2.a_c |
$2$ |
$\F_{2}$ |
$2$ |
$1 + 2 x^{2} + 4 x^{4}$ |
$0$ |
$2$ |
$3$ |
$7$ |
simple |
2.2.a_e |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 + 2 x^{2} )^{2}$ |
$0$ |
$2$ |
$3$ |
$9$ |
1.2.a 2 |
2.2.c_c |
$2$ |
$\F_{2}$ |
$2$ |
$1 + 2 x + 2 x^{2} + 4 x^{3} + 4 x^{4}$ |
$0$ |
$2$ |
$5$ |
$13$ |
simple |
2.2.c_e |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ |
$0$ |
$2$ |
$5$ |
$15$ |
1.2.a $\times$ 1.2.c |
2.2.e_i |
$2$ |
$\F_{2}$ |
$2$ |
$( 1 + 2 x + 2 x^{2} )^{2}$ |
$0$ |
$2$ |
$7$ |
$25$ |
1.2.c 2 |
2.3.ag_p |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 - 3 x + 3 x^{2} )^{2}$ |
$0$ |
$2$ |
$-2$ |
$1$ |
1.3.ad 2 |
2.3.ad_g |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$ |
$0$ |
$2$ |
$1$ |
$4$ |
1.3.ad $\times$ 1.3.a |
2.3.a_ag |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 - 3 x^{2} )^{2}$ |
$0$ |
$2$ |
$4$ |
$4$ |
simple |
2.3.a_ad |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 - 3 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$ |
$0$ |
$2$ |
$4$ |
$7$ |
1.3.ad $\times$ 1.3.d |
2.3.a_a |
$2$ |
$\F_{3}$ |
$3$ |
$1 + 9 x^{4}$ |
$0$ |
$2$ |
$4$ |
$10$ |
simple |
2.3.a_d |
$2$ |
$\F_{3}$ |
$3$ |
$1 + 3 x^{2} + 9 x^{4}$ |
$0$ |
$2$ |
$4$ |
$13$ |
simple |
2.3.a_g |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 + 3 x^{2} )^{2}$ |
$0$ |
$2$ |
$4$ |
$16$ |
1.3.a 2 |
2.3.d_g |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$ |
$0$ |
$2$ |
$7$ |
$28$ |
1.3.a $\times$ 1.3.d |
2.3.g_p |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 + 3 x + 3 x^{2} )^{2}$ |
$0$ |
$2$ |
$10$ |
$49$ |
1.3.d 2 |
2.4.ai_y |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x )^{4}$ |
$0$ |
$2$ |
$-3$ |
$1$ |
1.4.ae 2 |
2.4.ag_q |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x )^{2}( 1 - 2 x + 4 x^{2} )$ |
$0$ |
$2$ |
$-1$ |
$3$ |
1.4.ae $\times$ 1.4.ac |
2.4.ae_i |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x )^{2}( 1 + 4 x^{2} )$ |
$0$ |
$2$ |
$1$ |
$5$ |
1.4.ae $\times$ 1.4.a |
2.4.ae_m |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x + 4 x^{2} )^{2}$ |
$0$ |
$2$ |
$1$ |
$9$ |
1.4.ac 2 |
2.4.ac_a |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x )^{2}( 1 + 2 x + 4 x^{2} )$ |
$0$ |
$2$ |
$3$ |
$7$ |
1.4.ae $\times$ 1.4.c |
2.4.ac_e |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4}$ |
$0$ |
$2$ |
$3$ |
$11$ |
simple |
2.4.ac_i |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x + 4 x^{2} )( 1 + 4 x^{2} )$ |
$0$ |
$2$ |
$3$ |
$15$ |
1.4.ac $\times$ 1.4.a |
2.4.a_ai |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x )^{2}( 1 + 2 x )^{2}$ |
$0$ |
$2$ |
$5$ |
$9$ |
1.4.ae $\times$ 1.4.e |
2.4.a_ae |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$1 - 4 x^{2} + 16 x^{4}$ |
$0$ |
$2$ |
$5$ |
$13$ |
simple |
2.4.a_a |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$1 + 16 x^{4}$ |
$0$ |
$2$ |
$5$ |
$17$ |
simple |
2.4.a_e |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 - 2 x + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$ |
$0$ |
$2$ |
$5$ |
$21$ |
1.4.ac $\times$ 1.4.c |
2.4.a_i |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 4 x^{2} )^{2}$ |
$0$ |
$2$ |
$5$ |
$25$ |
1.4.a 2 |
2.4.c_a |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 2 x )^{2}( 1 - 2 x + 4 x^{2} )$ |
$0$ |
$2$ |
$7$ |
$27$ |
1.4.ac $\times$ 1.4.e |
2.4.c_e |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4}$ |
$0$ |
$2$ |
$7$ |
$31$ |
simple |
2.4.c_i |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$ |
$0$ |
$2$ |
$7$ |
$35$ |
1.4.a $\times$ 1.4.c |
2.4.e_i |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 2 x )^{2}( 1 + 4 x^{2} )$ |
$0$ |
$2$ |
$9$ |
$45$ |
1.4.a $\times$ 1.4.e |
2.4.e_m |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 2 x + 4 x^{2} )^{2}$ |
$0$ |
$2$ |
$9$ |
$49$ |
1.4.c 2 |
2.4.g_q |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 2 x )^{2}( 1 + 2 x + 4 x^{2} )$ |
$0$ |
$2$ |
$11$ |
$63$ |
1.4.c $\times$ 1.4.e |
2.4.i_y |
$2$ |
$\F_{2^{2}}$ |
$2$ |
$( 1 + 2 x )^{4}$ |
$0$ |
$2$ |
$13$ |
$81$ |
1.4.e 2 |
2.5.af_p |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4}$ |
$0$ |
$2$ |
$1$ |
$11$ |
simple |
2.5.a_ak |
$2$ |
$\F_{5}$ |
$5$ |
$( 1 - 5 x^{2} )^{2}$ |
$0$ |
$2$ |
$6$ |
$16$ |
simple |
2.5.a_af |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 5 x^{2} + 25 x^{4}$ |
$0$ |
$2$ |
$6$ |
$21$ |
simple |
2.5.a_a |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 25 x^{4}$ |
$0$ |
$2$ |
$6$ |
$26$ |
simple |
2.5.a_f |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 5 x^{2} + 25 x^{4}$ |
$0$ |
$2$ |
$6$ |
$31$ |
simple |
2.5.a_k |
$2$ |
$\F_{5}$ |
$5$ |
$( 1 + 5 x^{2} )^{2}$ |
$0$ |
$2$ |
$6$ |
$36$ |
1.5.a 2 |
2.5.f_p |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 5 x + 15 x^{2} + 25 x^{3} + 25 x^{4}$ |
$0$ |
$2$ |
$11$ |
$71$ |
simple |
2.7.a_ao |
$2$ |
$\F_{7}$ |
$7$ |
$( 1 - 7 x^{2} )^{2}$ |
$0$ |
$2$ |
$8$ |
$36$ |
simple |
2.7.a_ah |
$2$ |
$\F_{7}$ |
$7$ |
$1 - 7 x^{2} + 49 x^{4}$ |
$0$ |
$2$ |
$8$ |
$43$ |
simple |
2.7.a_a |
$2$ |
$\F_{7}$ |
$7$ |
$1 + 49 x^{4}$ |
$0$ |
$2$ |
$8$ |
$50$ |
simple |
2.7.a_h |
$2$ |
$\F_{7}$ |
$7$ |
$1 + 7 x^{2} + 49 x^{4}$ |
$0$ |
$2$ |
$8$ |
$57$ |
simple |