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 |
1.25.ak |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$( 1 - 5 x )^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$16$ |
$[16, 576, 15376, 389376, 9759376, 244109376, 6103359376, 152587109376, 3814693359376, 95367412109376]$ |
$16$ |
$[16, 576, 15376, 389376, 9759376, 244109376, 6103359376, 152587109376, 3814693359376, 95367412109376]$ |
$1$ |
$1$ |
$4$ |
$6$ |
$1$ |
\(\Q\) |
Trivial |
simple |
1.25.aj |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$17$ |
$[17, 595, 15572, 390915, 9769577, 244168960, 6103671857, 152588588355, 3814699639412, 95367435561475]$ |
$17$ |
$[17, 595, 15572, 390915, 9769577, 244168960, 6103671857, 152588588355, 3814699639412, 95367435561475]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
1.25.ai |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$18$ |
$[18, 612, 15714, 391680, 9771858, 244164132, 6103547874, 152587560960, 3814693822098, 95367412334052]$ |
$18$ |
$[18, 612, 15714, 391680, 9771858, 244164132, 6103547874, 152587560960, 3814693822098, 95367412334052]$ |
$3$ |
$3$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.25.ah |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$19$ |
$[19, 627, 15808, 391875, 9769819, 244138752, 6103397683, 152587111875, 3814694762944, 95367433590627]$ |
$19$ |
$[19, 627, 15808, 391875, 9769819, 244138752, 6103397683, 152587111875, 3814694762944, 95367433590627]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
simple |
1.25.ag |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
|
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$20$ |
$[20, 640, 15860, 391680, 9766100, 244117120, 6103362740, 152587560960, 3814699109780, 95367450947200]$ |
$20$ |
$[20, 640, 15860, 391680, 9766100, 244117120, 6103362740, 152587560960, 3814699109780, 95367450947200]$ |
$4$ |
$4$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.25.af |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 - 5 x + 25 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$21$ |
$[21, 651, 15876, 391251, 9762501, 244109376, 6103437501, 152588281251, 3814701171876, 95367441406251]$ |
$21$ |
$[21, 651, 15876, 391251, 9762501, 244109376, 6103437501, 152588281251, 3814701171876, 95367441406251]$ |
$2$ |
$2$ |
$4$ |
$6$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
1.25.ae |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$22$ |
$[22, 660, 15862, 390720, 9760102, 244116180, 6103555942, 152588663040, 3814699347382, 95367420657300]$ |
$22$ |
$[22, 660, 15862, 390720, 9760102, 244116180, 6103555942, 152588663040, 3814699347382, 95367420657300]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-21}) \) |
$C_2$ |
simple |
1.25.ad |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$23$ |
$[23, 667, 15824, 390195, 9759383, 244132672, 6103647839, 152588486115, 3814695746768, 95367412196827]$ |
$23$ |
$[23, 667, 15824, 390195, 9759383, 244132672, 6103647839, 152588486115, 3814695746768, 95367412196827]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
simple |
1.25.ac |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$24$ |
$[24, 672, 15768, 389760, 9760344, 244151712, 6103669848, 152587921920, 3814693472664, 95367423272352]$ |
$24$ |
$[24, 672, 15768, 389760, 9760344, 244151712, 6103669848, 152587921920, 3814693472664, 95367423272352]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-6}) \) |
$C_2$ |
simple |
1.25.ab |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$25$ |
$[25, 675, 15700, 389475, 9762625, 244166400, 6103616425, 152587347075, 3814694202100, 95367442165875]$ |
$25$ |
$[25, 675, 15700, 389475, 9762625, 244166400, 6103616425, 152587347075, 3814694202100, 95367442165875]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
1.25.b |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
|
✓ |
|
|
✓ |
✓ |
$1 + x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$27$ |
$[27, 675, 15552, 389475, 9768627, 244166400, 6103414827, 152587347075, 3814700329152, 95367442165875]$ |
$27$ |
$[27, 675, 15552, 389475, 9768627, 244166400, 6103414827, 152587347075, 3814700329152, 95367442165875]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
1.25.c |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$28$ |
$[28, 672, 15484, 389760, 9770908, 244151712, 6103361404, 152587921920, 3814701058588, 95367423272352]$ |
$28$ |
$[28, 672, 15484, 389760, 9770908, 244151712, 6103361404, 152587921920, 3814701058588, 95367423272352]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-6}) \) |
$C_2$ |
simple |
1.25.d |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$29$ |
$[29, 667, 15428, 390195, 9771869, 244132672, 6103383413, 152588486115, 3814698784484, 95367412196827]$ |
$29$ |
$[29, 667, 15428, 390195, 9771869, 244132672, 6103383413, 152588486115, 3814698784484, 95367412196827]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
simple |
1.25.e |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$30$ |
$[30, 660, 15390, 390720, 9771150, 244116180, 6103475310, 152588663040, 3814695183870, 95367420657300]$ |
$30$ |
$[30, 660, 15390, 390720, 9771150, 244116180, 6103475310, 152588663040, 3814695183870, 95367420657300]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-21}) \) |
$C_2$ |
simple |
1.25.f |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 5 x + 25 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$31$ |
$[31, 651, 15376, 391251, 9768751, 244109376, 6103593751, 152588281251, 3814693359376, 95367441406251]$ |
$31$ |
$[31, 651, 15376, 391251, 9768751, 244109376, 6103593751, 152588281251, 3814693359376, 95367441406251]$ |
$2$ |
$2$ |
$4$ |
$6$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
1.25.g |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
|
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$32$ |
$[32, 640, 15392, 391680, 9765152, 244117120, 6103668512, 152587560960, 3814695421472, 95367450947200]$ |
$32$ |
$[32, 640, 15392, 391680, 9765152, 244117120, 6103668512, 152587560960, 3814695421472, 95367450947200]$ |
$4$ |
$4$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.25.h |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$33$ |
$[33, 627, 15444, 391875, 9761433, 244138752, 6103633569, 152587111875, 3814699768308, 95367433590627]$ |
$33$ |
$[33, 627, 15444, 391875, 9761433, 244138752, 6103633569, 152587111875, 3814699768308, 95367433590627]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
simple |
1.25.i |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 8 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$34$ |
$[34, 612, 15538, 391680, 9759394, 244164132, 6103483378, 152587560960, 3814700709154, 95367412334052]$ |
$34$ |
$[34, 612, 15538, 391680, 9759394, 244164132, 6103483378, 152587560960, 3814700709154, 95367412334052]$ |
$3$ |
$3$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.25.j |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
|
✓ |
|
|
✓ |
✓ |
$1 + 9 x + 25 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$35$ |
$[35, 595, 15680, 390915, 9761675, 244168960, 6103359395, 152588588355, 3814694891840, 95367435561475]$ |
$35$ |
$[35, 595, 15680, 390915, 9761675, 244168960, 6103359395, 152588588355, 3814694891840, 95367435561475]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
1.25.k |
$1$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
|
|
✓ |
✓ |
✓ |
✓ |
$( 1 + 5 x )^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$36$ |
$[36, 576, 15876, 389376, 9771876, 244109376, 6103671876, 152587109376, 3814701171876, 95367412109376]$ |
$36$ |
$[36, 576, 15876, 389376, 9771876, 244109376, 6103671876, 152587109376, 3814701171876, 95367412109376]$ |
$1$ |
$1$ |
$4$ |
$6$ |
$1$ |
\(\Q\) |
Trivial |
simple |