| Label |
Dimension |
Base field |
Base char. |
Simple |
Geom. simple |
Primitive |
Ordinary |
Almost ordinary |
Supersingular |
Princ. polarizable |
Jacobian |
L-polynomial |
Newton slopes |
Newton elevation |
$p$-rank |
$p$-corank |
Angle rank |
Angle corank |
$\mathbb{F}_q$ points on curve |
$\mathbb{F}_{q^k}$ points on curve |
$\mathbb{F}_q$ points on variety |
$\mathbb{F}_{q^k}$ points on variety |
Jacobians |
Hyperelliptic Jacobians |
Num. twists |
Max. twist degree |
End. degree |
Number fields |
Galois groups |
Isogeny factors |
| 1.13.ah |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$7$ |
$[7, 147, 2128, 28371, 370867, 4826304, 62750527, 815751363, 10604617744, 137859052107]$ |
$7$ |
$[7, 147, 2128, 28371, 370867, 4826304, 62750527, 815751363, 10604617744, 137859052107]$ |
$1$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.13.ag |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$8$ |
$[8, 160, 2216, 28800, 372488, 4830880, 62757416, 815731200, 10604386568, 137857808800]$ |
$8$ |
$[8, 160, 2216, 28800, 372488, 4830880, 62757416, 815731200, 10604386568, 137857808800]$ |
$2$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.13.af |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$9$ |
$[9, 171, 2268, 28899, 372069, 4826304, 62735913, 815674275, 10604381004, 137858633811]$ |
$9$ |
$[9, 171, 2268, 28899, 372069, 4826304, 62735913, 815674275, 10604381004, 137858633811]$ |
$2$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.13.ae |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$10$ |
$[10, 180, 2290, 28800, 371050, 4822740, 62735410, 815731200, 10604671690, 137859174900]$ |
$10$ |
$[10, 180, 2290, 28800, 371050, 4822740, 62735410, 815731200, 10604671690, 137859174900]$ |
$3$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.13.ad |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$11$ |
$[11, 187, 2288, 28611, 370271, 4823104, 62750699, 815785443, 10604635184, 137858187907]$ |
$11$ |
$[11, 187, 2288, 28611, 370271, 4823104, 62750699, 815785443, 10604635184, 137858187907]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
| 1.13.ac |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$12$ |
$[12, 192, 2268, 28416, 370092, 4826304, 62763132, 815766528, 10604381004, 137857789632]$ |
$12$ |
$[12, 192, 2268, 28416, 370092, 4826304, 62763132, 815766528, 10604381004, 137857789632]$ |
$4$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.13.ab |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$13$ |
$[13, 195, 2236, 28275, 370513, 4829760, 62761621, 815705475, 10604303788, 137858624475]$ |
$13$ |
$[13, 195, 2236, 28275, 370513, 4829760, 62761621, 815705475, 10604303788, 137858624475]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
simple |
| 1.13.a |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 13 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$14$ |
$[14, 196, 2198, 28224, 371294, 4831204, 62748518, 815673600, 10604499374, 137859234436]$ |
$14$ |
$[14, 196, 2198, 28224, 371294, 4831204, 62748518, 815673600, 10604499374, 137859234436]$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
$C_2$ |
simple |
| 1.13.b |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$15$ |
$[15, 195, 2160, 28275, 372075, 4829760, 62735415, 815705475, 10604694960, 137858624475]$ |
$15$ |
$[15, 195, 2160, 28275, 372075, 4829760, 62735415, 815705475, 10604694960, 137858624475]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
simple |
| 1.13.c |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$16$ |
$[16, 192, 2128, 28416, 372496, 4826304, 62733904, 815766528, 10604617744, 137857789632]$ |
$16$ |
$[16, 192, 2128, 28416, 372496, 4826304, 62733904, 815766528, 10604617744, 137857789632]$ |
$4$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.13.d |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$17$ |
$[17, 187, 2108, 28611, 372317, 4823104, 62746337, 815785443, 10604363564, 137858187907]$ |
$17$ |
$[17, 187, 2108, 28611, 372317, 4823104, 62746337, 815785443, 10604363564, 137858187907]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
| 1.13.e |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$18$ |
$[18, 180, 2106, 28800, 371538, 4822740, 62761626, 815731200, 10604327058, 137859174900]$ |
$18$ |
$[18, 180, 2106, 28800, 371538, 4822740, 62761626, 815731200, 10604327058, 137859174900]$ |
$3$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.13.f |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$19$ |
$[19, 171, 2128, 28899, 370519, 4826304, 62761123, 815674275, 10604617744, 137858633811]$ |
$19$ |
$[19, 171, 2128, 28899, 370519, 4826304, 62761123, 815674275, 10604617744, 137858633811]$ |
$2$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.13.g |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$20$ |
$[20, 160, 2180, 28800, 370100, 4830880, 62739620, 815731200, 10604612180, 137857808800]$ |
$20$ |
$[20, 160, 2180, 28800, 370100, 4830880, 62739620, 815731200, 10604612180, 137857808800]$ |
$2$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.13.h |
$1$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 13 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$21$ |
$[21, 147, 2268, 28371, 371721, 4826304, 62746509, 815751363, 10604381004, 137859052107]$ |
$21$ |
$[21, 147, 2268, 28371, 371721, 4826304, 62746509, 815751363, 10604381004, 137859052107]$ |
$1$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |