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.ae_i |
$2$ |
$\F_{3}$ |
$3$ |
$1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4}$ |
$2$ |
$0$ |
$0$ |
$2$ |
simple |
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.ac_b |
$2$ |
$\F_{3}$ |
$3$ |
$1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4}$ |
$2$ |
$0$ |
$2$ |
$3$ |
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.c_b |
$2$ |
$\F_{3}$ |
$3$ |
$1 + 2 x + x^{2} + 6 x^{3} + 9 x^{4}$ |
$2$ |
$0$ |
$6$ |
$19$ |
simple |
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.e_i |
$2$ |
$\F_{3}$ |
$3$ |
$1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4}$ |
$2$ |
$0$ |
$8$ |
$34$ |
simple |
2.3.g_p |
$2$ |
$\F_{3}$ |
$3$ |
$( 1 + 3 x + 3 x^{2} )^{2}$ |
$0$ |
$2$ |
$10$ |
$49$ |
1.3.d 2 |
2.5.ag_r |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$0$ |
$7$ |
simple |
2.5.ae_i |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$2$ |
$10$ |
simple |
2.5.ae_l |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$2$ |
$13$ |
simple |
2.5.ac_ab |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 2 x - x^{2} - 10 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$4$ |
$13$ |
simple |
2.5.a_ai |
$2$ |
$\F_{5}$ |
$5$ |
$1 - 8 x^{2} + 25 x^{4}$ |
$2$ |
$0$ |
$6$ |
$18$ |
simple |
2.5.a_i |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 8 x^{2} + 25 x^{4}$ |
$2$ |
$0$ |
$6$ |
$34$ |
simple |
2.5.c_ab |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 2 x - x^{2} + 10 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$8$ |
$37$ |
simple |
2.5.e_i |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 4 x + 8 x^{2} + 20 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$10$ |
$58$ |
simple |
2.5.e_l |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 4 x + 11 x^{2} + 20 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$10$ |
$61$ |
simple |
2.5.g_r |
$2$ |
$\F_{5}$ |
$5$ |
$1 + 6 x + 17 x^{2} + 30 x^{3} + 25 x^{4}$ |
$2$ |
$0$ |
$12$ |
$79$ |
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 |
2.8.ai_bg |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 - 4 x + 8 x^{2} )^{2}$ |
$0$ |
$2$ |
$1$ |
$25$ |
1.8.ae 2 |
2.8.ae_i |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$1 - 4 x + 8 x^{2} - 32 x^{3} + 64 x^{4}$ |
$0$ |
$2$ |
$5$ |
$37$ |
simple |
2.8.ae_q |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 - 4 x + 8 x^{2} )( 1 + 8 x^{2} )$ |
$0$ |
$2$ |
$5$ |
$45$ |
1.8.ae $\times$ 1.8.a |
2.8.a_aq |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 - 8 x^{2} )^{2}$ |
$0$ |
$2$ |
$9$ |
$49$ |
simple |
2.8.a_ai |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$1 - 8 x^{2} + 64 x^{4}$ |
$0$ |
$2$ |
$9$ |
$57$ |
simple |
2.8.a_a |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 - 4 x + 8 x^{2} )( 1 + 4 x + 8 x^{2} )$ |
$0$ |
$2$ |
$9$ |
$65$ |
1.8.ae $\times$ 1.8.e |
2.8.a_i |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$1 + 8 x^{2} + 64 x^{4}$ |
$0$ |
$2$ |
$9$ |
$73$ |
simple |
2.8.a_q |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 + 8 x^{2} )^{2}$ |
$0$ |
$2$ |
$9$ |
$81$ |
1.8.a 2 |
2.8.e_i |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$1 + 4 x + 8 x^{2} + 32 x^{3} + 64 x^{4}$ |
$0$ |
$2$ |
$13$ |
$109$ |
simple |
2.8.e_q |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 + 8 x^{2} )( 1 + 4 x + 8 x^{2} )$ |
$0$ |
$2$ |
$13$ |
$117$ |
1.8.a $\times$ 1.8.e |
2.8.i_bg |
$2$ |
$\F_{2^{3}}$ |
$2$ |
$( 1 + 4 x + 8 x^{2} )^{2}$ |
$0$ |
$2$ |
$17$ |
$169$ |
1.8.e 2 |
2.9.ai_bg |
$2$ |
$\F_{3^{2}}$ |
$3$ |
$1 - 8 x + 32 x^{2} - 72 x^{3} + 81 x^{4}$ |
$2$ |
$0$ |
$2$ |
$34$ |
simple |
2.9.ac_af |
$2$ |
$\F_{3^{2}}$ |
$3$ |
$1 - 2 x - 5 x^{2} - 18 x^{3} + 81 x^{4}$ |
$2$ |
$0$ |
$8$ |
$57$ |
simple |
2.9.c_af |
$2$ |
$\F_{3^{2}}$ |
$3$ |
$1 + 2 x - 5 x^{2} + 18 x^{3} + 81 x^{4}$ |
$2$ |
$0$ |
$12$ |
$97$ |
simple |
2.9.i_bg |
$2$ |
$\F_{3^{2}}$ |
$3$ |
$1 + 8 x + 32 x^{2} + 72 x^{3} + 81 x^{4}$ |
$2$ |
$0$ |
$18$ |
$194$ |
simple |