| 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 |
| 2.25.au_fu |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
|
|
|
✓ |
✓ |
✓ |
$( 1 - 5 x )^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$6$ |
$[6, 526, 15126, 388126, 9753126, 244078126, 6103203126, 152586328126, 3814689453126, 95367392578126]$ |
$256$ |
$[256, 331776, 236421376, 151613669376, 95245419909376, 59589387451109376, 37250995672607109376, 23282825947723387109376, 14551885426067352287109376, 9094943292439556121787109376]$ |
$1$ |
$1$ |
$15$ |
$12$ |
$1$ |
\(\Q\) |
Trivial |
1.25.ak 2 |
| 2.25.at_fk |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x )^{2}( 1 - 9 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$7$ |
$[7, 545, 15322, 389665, 9763327, 244137710, 6103515607, 152587807105, 3814695733162, 95367416030225]$ |
$272$ |
$[272, 342720, 239435072, 152212919040, 95344975303952, 59603932464168960, 37252902856448281232, 23283051620853824916480, 14551909382478978129326912, 9094945529005546284671889600]$ |
$0$ |
$0$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-19}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.aj |
| 2.25.as_fa |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x )^{2}( 1 - 8 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$8$ |
$[8, 562, 15464, 390430, 9765608, 244132882, 6103391624, 152586779710, 3814689915848, 95367392802802]$ |
$288$ |
$[288, 352512, 241618464, 152510791680, 95367236440608, 59602753904101632, 37252146143642766624, 23282894853620587560960, 14551887191209892924290848, 9094943313866324804873271552]$ |
$0$ |
$0$ |
$16$ |
$12$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-1}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.ai |
| 2.25.as_fb |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 25 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 564, 15518, 391204, 9773528, 244197294, 6103828088, 152589286084, 3814702013198, 95367439482324]$ |
$289$ |
$[289, 354025, 242487184, 152814537225, 95444634758929, 59618481027481600, 37254810137933828449, 23283277296171641606025, 14551933338930042823705744, 9094947765572086448504175625]$ |
$1$ |
$1$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
1.25.aj 2 |
| 2.25.ar_eq |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x )^{2}( 1 - 7 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$9$ |
$[9, 577, 15558, 390625, 9763569, 244107502, 6103241433, 152586330625, 3814690856694, 95367414059377]$ |
$304$ |
$[304, 361152, 243063808, 152586720000, 95347337072944, 59596558408138752, 37251229473994725808, 23282826329038573440000, 14551890780248881319762944, 9094945341050872863732418752]$ |
$0$ |
$0$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-51}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.ah |
| 2.25.ar_er |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 121 x^{2} - 425 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 579, 15609, 391299, 9769774, 244151859, 6103501329, 152587630659, 3814696757649, 95367441364174]$ |
$305$ |
$[305, 362645, 243880745, 152850878405, 95407952922000, 59607387719481605, 37252815730859812745, 23283024697531434104645, 14551913290584695922143105, 9094947945039117554393088000]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.8525.1 |
$D_{4}$ |
simple |
| 2.25.ar_es |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 25 x^{2} )( 1 - 8 x + 25 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 581, 15660, 391969, 9775809, 244192466, 6103704105, 152588258689, 3814696195884, 95367416254901]$ |
$306$ |
$[306, 364140, 244698408, 153113587200, 95466919164066, 59617302179742720, 37254053386385982018, 23283120527418908620800, 14551911147624424677326376, 9094945550432320236881846700]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.25.aj $\times$ 1.25.ai |
| 2.25.aq_eg |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 5 x )^{2}( 1 - 6 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$10$ |
$[10, 590, 15610, 390430, 9759850, 244085870, 6103206490, 152586779710, 3814695203530, 95367431415950]$ |
$320$ |
$[320, 368640, 243863360, 152510791680, 95311041953600, 59591277834117120, 37251016204308050240, 23282894853620587560960, 14551907362095304816297280, 9094946996302322961200947200]$ |
$3$ |
$3$ |
$16$ |
$12$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-1}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.ag |
| 2.25.aq_eh |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 111 x^{2} - 400 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 592, 15658, 391012, 9764650, 244116214, 6103367770, 152587603012, 3814699921018, 95367462167152]$ |
$321$ |
$[321, 370113, 244628964, 152738602953, 95357916129201, 59598685407459600, 37252000554119507841, 23283020479166964777993, 14551925357892480474958884, 9094949928966083773271598753]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.46224.1 |
$D_{4}$ |
simple |
| 2.25.aq_ei |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 112 x^{2} - 400 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 594, 15706, 391590, 9769290, 244143282, 6103483354, 152587939902, 3814700440906, 95367462357394]$ |
$322$ |
$[322, 371588, 245395234, 152964943376, 95403234965122, 59605293521677316, 37252706006959595362, 23283071884126425448448, 14551927341103578433921858, 9094949947108970491607060868]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.41216.1 |
$D_{4}$ |
simple |
| 2.25.aq_ej |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 25 x^{2} )( 1 - 7 x + 25 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 596, 15754, 392164, 9773770, 244167086, 6103553914, 152587809604, 3814697136730, 95367437511476]$ |
$323$ |
$[323, 373065, 246162176, 153189815625, 95446998996563, 59611105171537920, 37253136669806107331, 23283052002172707215625, 14551914736669321619548928, 9094947577617366807042294825]$ |
$6$ |
$6$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.25.aj $\times$ 1.25.ah |
| 2.25.aq_ek |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 25 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$10$ |
$[10, 598, 15802, 392734, 9778090, 244187638, 6103580122, 152587231294, 3814690378570, 95367393027478]$ |
$324$ |
$[324, 374544, 246929796, 153413222400, 95489208772164, 59616123355313424, 37253296650209919876, 23282963759721716121600, 14551888956352647673121604, 9094943335293093538438738704]$ |
$5$ |
$5$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.25.ai 2 |
| 2.25.ap_dw |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 5 x )^{2}( 1 - 5 x + 25 x^{2} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$11$ |
$[11, 601, 15626, 390001, 9756251, 244078126, 6103281251, 152587500001, 3814697265626, 95367421875001]$ |
$336$ |
$[336, 374976, 244109376, 152343749376, 95275917959376, 59589387451109376, 37251472497558359376, 23283004760742187109376, 14551915228359222412109376, 9094946086406707763662109376]$ |
$0$ |
$0$ |
$15$ |
$30$ |
$6$ |
\(\Q\), \(\Q(\sqrt{-3}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.af |
| 2.25.ap_dx |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 101 x^{2} - 375 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$11$ |
$[11, 603, 15671, 390499, 9759926, 244099203, 6103394231, 152588195299, 3814702125491, 95367454132878]$ |
$337$ |
$[337, 376429, 244824097, 152538441525, 95311795063552, 59594532551290429, 37252162062695608057, 23283110855115667066725, 14551933767292198562477017, 9094949162757899359443349504]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.132741.1 |
$D_{4}$ |
simple |
| 2.25.ap_dy |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 102 x^{2} - 375 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$11$ |
$[11, 605, 15716, 390993, 9763451, 244117442, 6103471091, 152588542369, 3814704249716, 95367467713565]$ |
$338$ |
$[338, 377884, 245539424, 152731643584, 95346211805858, 59598984911155456, 37252631167549945394, 23283163813831131974400, 14551941870575701453548128, 9094950457913341110674535964]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.174556.1 |
$D_{4}$ |
simple |
| 2.25.ap_dz |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 103 x^{2} - 375 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$11$ |
$[11, 607, 15761, 391483, 9766826, 244132855, 6103512461, 152588557939, 3814703937191, 95367466650862]$ |
$339$ |
$[339, 379341, 246255363, 152923357989, 95379168616944, 59602747504657509, 37252883660218189323, 23283166189492641874725, 14551940678386160560834899, 9094950356566065596123233536]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.153621.1 |
$D_{4}$ |
simple |
| 2.25.ap_ea |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 25 x^{2} )( 1 - 6 x + 25 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$11$ |
$[11, 609, 15806, 391969, 9770051, 244145454, 6103518971, 152588258689, 3814701483566, 95367454868049]$ |
$340$ |
$[340, 380800, 246971920, 153113587200, 95410665939700, 59605823308595200, 37252923389200408180, 23283120527418908620800, 14551931318543043402649360, 9094949232869223952579120000]$ |
$7$ |
$7$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.25.aj $\times$ 1.25.ag |
| 2.25.ap_ec |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 25 x^{2} )( 1 - 7 x + 25 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$11$ |
$[11, 613, 15896, 392929, 9776051, 244162258, 6103429931, 152586782209, 3814691319416, 95367414284053]$ |
$342$ |
$[342, 383724, 248406912, 153489600000, 95469283953702, 59609926469643264, 37252379952251175942, 23282895234936902400000, 14551892545392071418736512, 9094945362477646373140130604]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.25.ai $\times$ 1.25.ah |
| 2.25.ao_dm |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x )^{2}( 1 - 4 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$12$ |
$[12, 610, 15612, 389470, 9753852, 244084930, 6103399692, 152587881790, 3814695441132, 95367401126050]$ |
$352$ |
$[352, 380160, 243894112, 152136990720, 95252505216352, 59591048371303680, 37252195385546212192, 23283063016822088663040, 14551908268474076390753632, 9094944107632946909412844800]$ |
$0$ |
$0$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-21}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.ae |
| 2.25.ao_dn |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 91 x^{2} - 350 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 612, 15654, 389892, 9756652, 244100334, 6103493772, 152588569092, 3814700259414, 95367429346852]$ |
$353$ |
$[353, 381593, 244558400, 152301779753, 95279834032353, 59594808715289600, 37252769609748663953, 23283167891337444355913, 14551926648770383513217600, 9094946798978095397586825753]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.17984.1 |
$D_{4}$ |
simple |
| 2.25.ao_do |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 92 x^{2} - 350 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 614, 15696, 390310, 9759312, 244113302, 6103559628, 152589008062, 3814703244396, 95367445017494]$ |
$354$ |
$[354, 383028, 245223234, 152465061456, 95305798099794, 59597974337790996, 37253171563634889426, 23283234873186725680128, 14551938035580978069408018, 9094948293446947741852666068]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.442176.2 |
$D_{4}$ |
simple |
| 2.25.ao_dp |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 93 x^{2} - 350 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 616, 15738, 390724, 9761832, 244123846, 6103597848, 152589213124, 3814704632202, 95367451045576]$ |
$355$ |
$[355, 384465, 245888620, 152626838025, 95330397755275, 59600548196453520, 37253404837310604955, 23283266163308436585225, 14551943329645338185101420, 9094948868329720187074539825]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.489024.2 |
$D_{4}$ |
simple |
| 2.25.ao_dq |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 94 x^{2} - 350 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 618, 15780, 391134, 9764212, 244131978, 6103609020, 152589198654, 3814704655932, 95367450243178]$ |
$356$ |
$[356, 385904, 246554564, 152787111680, 95353633346436, 59602533251174384, 37253473021149890084, 23283263955337086955520, 14551943420168216498955236, 9094948791807146374566373104]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.28400.1 |
$D_{4}$ |
simple |
| 2.25.ao_dr |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 9 x + 25 x^{2} )( 1 - 5 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$12$ |
$[12, 620, 15822, 391540, 9766452, 244137710, 6103593732, 152588978980, 3814703545662, 95367445327100]$ |
$357$ |
$[357, 387345, 247221072, 152945884665, 95375505232077, 59603932464168960, 37253379705812109357, 23283230435605803432105, 14551939184819911035576912, 9094948322973384999759780225]$ |
$4$ |
$4$ |
$8$ |
$6$ |
$3$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.25.aj $\times$ 1.25.af |
| 2.25.ao_ds |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 96 x^{2} - 350 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 622, 15864, 391942, 9768552, 244141054, 6103552572, 152588568382, 3814701528444, 95367438919102]$ |
$358$ |
$[358, 388788, 247888150, 153103159248, 95396013782278, 59604748800038100, 37253128482259302838, 23283167783149082784768, 14551931489736563015039350, 9094947711858931001642353428]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.247104.1 |
$D_{4}$ |
simple |
| 2.25.ao_dt |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 97 x^{2} - 350 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 624, 15906, 392340, 9770512, 244142022, 6103486128, 152587981092, 3814698828306, 95367433546144]$ |
$359$ |
$[359, 390233, 248555804, 153258937721, 95415159378519, 59604985225836176, 37252722941774050391, 23283078169705691603753, 14551921189520482934528348, 9094947199453530582488933193]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.128576.2 |
$D_{4}$ |
simple |
| 2.25.ao_du |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 25 x^{2} )( 1 - 6 x + 25 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$12$ |
$[12, 626, 15948, 392734, 9772332, 244140626, 6103394988, 152587231294, 3814695666252, 95367431640626]$ |
$360$ |
$[360, 391680, 249224040, 153413222400, 95432942413800, 59604644711139840, 37252166675977814760, 23282963759721716121600, 14551909127240506291918440, 9094947017729100370214054400]$ |
$10$ |
$10$ |
$16$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.25.ai $\times$ 1.25.ag |
| 2.25.ao_dv |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 25 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$12$ |
$[12, 628, 15990, 393124, 9774012, 244136878, 6103279740, 152586333124, 3814692260262, 95367435540628]$ |
$361$ |
$[361, 393129, 249892864, 153566015625, 95449363292761, 59603730228117504, 37251463276849768489, 23282826710353766015625, 14551896134432380355547136, 9094947389662651049822253129]$ |
$6$ |
$6$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
1.25.ah 2 |
| 2.25.an_dc |
$2$ |
$\F_{5^{2}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x )^{2}( 1 - 3 x + 25 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$13$ |
$[13, 617, 15574, 388945, 9753133, 244101422, 6103491589, 152587704865, 3814691840518, 95367392665577]$ |
$368$ |
$[368, 384192, 243309824, 151932568320, 95245488225008, 59595074223132672, 37252756265962788464, 23283036020347762314240, 14551894533235760914496768, 9094943300779531678164149952]$ |
$0$ |
$0$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-91}) \) |
Trivial, $C_2$ |
1.25.ak $\times$ 1.25.ad |
| 2.25.an_dd |
$2$ |
$\F_{5^{2}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 13 x + 81 x^{2} - 325 x^{3} + 625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$13$ |
$[13, 619, 15613, 389299, 9755278, 244113739, 6103581133, 152588386339, 3814696133053, 95367414858574]$ |
$369$ |
$[369, 385605, 243924129, 152070658245, 95266422092304, 59598081227842245, 37253302812836762769, 23283140005390547056005, 14551910907951479309927649, 9094945417268223266468352000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.6525.1 |
$D_{4}$ |
simple |
