| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 256.a.512.1 |
256.a |
\( 2^{8} \) |
\( - 2^{9} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$6$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,\frac{129623}{4},-\frac{1521}{8}]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 324.a.648.1 |
324.a |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[\frac{9375}{8},-\frac{625}{4},\frac{875}{18}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 388.a.776.1 |
388.a |
\( 2^{2} \cdot 97 \) |
\( 2^{3} \cdot 97 \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(29.135501\) |
\(0.198201\) |
$[36,1569,-13743,99328]$ |
$[9,-62,356,-160,776]$ |
$[\frac{59049}{776},-\frac{22599}{388},\frac{7209}{194}]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$ |
| 472.a.944.1 |
472.a |
\( 2^{3} \cdot 59 \) |
\( - 2^{4} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(29.113273\) |
\(0.227447\) |
$[280,760,60604,-3776]$ |
$[140,690,4544,40015,-944]$ |
$[-\frac{3361400000}{59},-\frac{118335000}{59},-\frac{5566400}{59}]$ |
$y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$ |
| 476.a.952.1 |
476.a |
\( 2^{2} \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 7 \cdot 17 \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(26.722339\) |
\(0.247429\) |
$[7340,1042345,2905273355,121856]$ |
$[1835,96870,-3910340,-4139817700,952]$ |
$[\frac{20805604708146875}{952},\frac{299272981175625}{476},-\frac{27661753375}{2}]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$ |
| 523.a.523.1 |
523.a |
\( 523 \) |
\( -523 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.819904\) |
\(0.248199\) |
$[120,-540,-29169,-2092]$ |
$[60,240,2241,19215,-523]$ |
$[-\frac{777600000}{523},-\frac{51840000}{523},-\frac{8067600}{523}]$ |
$y^2 + (x + 1)y = x^5 - x^4 - x^3$ |
| 523.a.523.2 |
523.a |
\( 523 \) |
\( -523 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.992796\) |
\(0.248199\) |
$[332400,10084860,1107044456391,-2092]$ |
$[166200,1149254190,10581558955401,109467476288772525,-523]$ |
$[-\frac{126810465636208320000000000}{523},-\frac{5276053055713522320000000}{523},-\frac{292288477352026798440000}{523}]$ |
$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$ |
| 529.a.529.1 |
529.a |
\( 23^{2} \) |
\( 23^{2} \) |
$0$ |
$0$ |
$\Z/11\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.120.2, 3.432.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.060256\) |
\(0.248432\) |
$[284,2401,246639,-67712]$ |
$[71,110,-624,-14101,-529]$ |
$[-\frac{1804229351}{529},-\frac{39370210}{529},\frac{3145584}{529}]$ |
$y^2 + (x^3 + x + 1)y = -x^5$ |
| 576.a.576.1 |
576.a |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.1080.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.396252\) |
\(0.223963\) |
$[68,124,2616,72]$ |
$[68,110,-36,-3637,576]$ |
$[\frac{22717712}{9},\frac{540430}{9},-289]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$ |
| 587.a.587.1 |
587.a |
\( 587 \) |
\( 587 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.003773\) |
\(29.510964\) |
\(0.111352\) |
$[60,1401,54147,-75136]$ |
$[15,-49,-501,-2479,-587]$ |
$[-\frac{759375}{587},\frac{165375}{587},\frac{112725}{587}]$ |
$y^2 + (x^3 + x + 1)y = -x^2 - x$ |
| 597.a.597.1 |
597.a |
\( 3 \cdot 199 \) |
\( 3 \cdot 199 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.411617\) |
\(0.294115\) |
$[120,192,9912,2388]$ |
$[60,118,-68,-4501,597]$ |
$[\frac{259200000}{199},\frac{8496000}{199},-\frac{81600}{199}]$ |
$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$ |
| 603.a.603.1 |
603.a |
\( 3^{2} \cdot 67 \) |
\( - 3^{2} \cdot 67 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[1672,75628,49887881,2412]$ |
$[836,16516,-1263521,-332270453,603]$ |
$[\frac{408348897330176}{603},\frac{9649919856896}{603},-\frac{883069772816}{603}]$ |
$y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$ |
| 603.a.603.2 |
603.a |
\( 3^{2} \cdot 67 \) |
\( - 3^{2} \cdot 67 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[176,148,7375,-2412]$ |
$[88,298,1361,7741,-603]$ |
$[-\frac{5277319168}{603},-\frac{203078656}{603},-\frac{10539584}{603}]$ |
$y^2 + (x^2 + 1)y = x^5 - x^3 + x$ |
| 686.a.686.1 |
686.a |
\( 2 \cdot 7^{3} \) |
\( 2 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.491655\) |
\(0.319213\) |
$[420,4305,640185,87808]$ |
$[105,280,-980,-45325,686]$ |
$[\frac{37209375}{2},472500,-15750]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$ |
| 691.a.691.1 |
691.a |
\( 691 \) |
\( -691 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.812569\) |
\(0.293946\) |
$[104,-824,-20333,-2764]$ |
$[52,250,601,-7812,-691]$ |
$[-\frac{380204032}{691},-\frac{35152000}{691},-\frac{1625104}{691}]$ |
$y^2 + (x + 1)y = x^5 - x^3 - x^2$ |
| 709.a.709.1 |
709.a |
\( 709 \) |
\( 709 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.361162\) |
\(0.286893\) |
$[160,-1280,-42089,2836]$ |
$[80,480,1121,-35180,709]$ |
$[\frac{3276800000}{709},\frac{245760000}{709},\frac{7174400}{709}]$ |
$y^2 + xy = x^5 - 2x^2 + x$ |
| 713.a.713.1 |
713.a |
\( 23 \cdot 31 \) |
\( 23 \cdot 31 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004592\) |
\(27.957889\) |
\(0.128395\) |
$[36,1305,-2547,91264]$ |
$[9,-51,173,-261,713]$ |
$[\frac{59049}{713},-\frac{37179}{713},\frac{14013}{713}]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x$ |
| 713.b.713.1 |
713.b |
\( 23 \cdot 31 \) |
\( 23 \cdot 31 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.149881\) |
\(0.285801\) |
$[92,73,6379,-91264]$ |
$[23,19,-41,-326,-713]$ |
$[-\frac{279841}{31},-\frac{10051}{31},\frac{943}{31}]$ |
$y^2 + (x^3 + x + 1)y = -x^4$ |
| 743.a.743.1 |
743.a |
\( 743 \) |
\( -743 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004577\) |
\(28.765391\) |
\(0.131656\) |
$[28,1945,15219,95104]$ |
$[7,-79,-53,-1653,743]$ |
$[\frac{16807}{743},-\frac{27097}{743},-\frac{2597}{743}]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2$ |
| 745.a.745.1 |
745.a |
\( 5 \cdot 149 \) |
\( - 5 \cdot 149 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.572840\) |
\(0.303368\) |
$[124,1417,38763,95360]$ |
$[31,-19,39,212,745]$ |
$[\frac{28629151}{745},-\frac{566029}{745},\frac{37479}{745}]$ |
$y^2 + (x^3 + x + 1)y = -x$ |
| 763.a.763.1 |
763.a |
\( 7 \cdot 109 \) |
\( - 7 \cdot 109 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.485750\) |
\(0.304858\) |
$[216,1116,75735,-3052]$ |
$[108,300,81,-20313,-763]$ |
$[-\frac{14693280768}{763},-\frac{377913600}{763},-\frac{944784}{763}]$ |
$y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x$ |
| 797.a.797.1 |
797.a |
\( 797 \) |
\( 797 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.440989\) |
\(0.355939\) |
$[24,528,7608,3188]$ |
$[12,-82,-548,-3325,797]$ |
$[\frac{248832}{797},-\frac{141696}{797},-\frac{78912}{797}]$ |
$y^2 + y = x^5 - x^4 + x^3$ |
| 832.a.832.1 |
832.a |
\( 2^{6} \cdot 13 \) |
\( - 2^{6} \cdot 13 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.148215\) |
\(0.330441\) |
$[272,-131,-12402,-104]$ |
$[272,3170,51008,956319,-832]$ |
$[-\frac{23262937088}{13},-\frac{996749440}{13},-\frac{58965248}{13}]$ |
$y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1$ |
| 841.a.841.1 |
841.a |
\( 29^{2} \) |
\( - 29^{2} \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.60.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.284557\) |
\(0.291522\) |
$[1420,4201,1973899,107648]$ |
$[355,5076,93408,1848516,841]$ |
$[\frac{5638216721875}{841},\frac{227094529500}{841},\frac{11771743200}{841}]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$ |
| 847.a.847.1 |
847.a |
\( 7 \cdot 11^{2} \) |
\( - 7 \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.196056\) |
\(20.305961\) |
\(0.159244\) |
$[120,276,6864,3388]$ |
$[60,104,504,4856,847]$ |
$[\frac{777600000}{847},\frac{22464000}{847},\frac{259200}{121}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$ |
| 847.d.847.1 |
847.d |
\( 7 \cdot 11^{2} \) |
\( - 7 \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(1.179535\) |
\(0.262119\) |
$[80408,402403732,8094753026048,3388]$ |
$[40204,281112,1967560,19956424,847]$ |
$[\frac{105037970421355597057024}{847},\frac{18267839107785466368}{847},\frac{454326923025280}{121}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$ |
| 862.a.862.1 |
862.a |
\( 2 \cdot 431 \) |
\( - 2 \cdot 431 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.926605\) |
\(0.373853\) |
$[1940,2609665,270472593,-110336]$ |
$[485,-98935,11156681,-1094285985,-862]$ |
$[-\frac{26835438303125}{862},\frac{11286912906875}{862},-\frac{2624330288225}{862}]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$ |
| 862.b.862.1 |
862.b |
\( 2 \cdot 431 \) |
\( 2 \cdot 431 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.488991\) |
\(0.339370\) |
$[552,696,112755,3448]$ |
$[276,3058,45033,769436,862]$ |
$[\frac{800784050688}{431},\frac{32146576704}{431},\frac{1715216904}{431}]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$ |
| 893.a.893.1 |
893.a |
\( 19 \cdot 47 \) |
\( 19 \cdot 47 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006429\) |
\(23.402435\) |
\(0.150459\) |
$[156,-519,-11805,-114304]$ |
$[39,85,67,-1153,-893]$ |
$[-\frac{90224199}{893},-\frac{5042115}{893},-\frac{101907}{893}]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2$ |
| 909.a.909.1 |
909.a |
\( 3^{2} \cdot 101 \) |
\( 3^{2} \cdot 101 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.805548\) |
\(0.340712\) |
$[40,-200,-5469,3636]$ |
$[20,50,441,1580,909]$ |
$[\frac{3200000}{909},\frac{400000}{909},\frac{19600}{101}]$ |
$y^2 + (x^3 + x)y = -x^4 + x^2 - x$ |
| 925.a.925.1 |
925.a |
\( 5^{2} \cdot 37 \) |
\( 5^{2} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.878934\) |
\(0.326233\) |
$[40,-944,-14117,3700]$ |
$[20,174,713,-4004,925]$ |
$[\frac{128000}{37},\frac{55680}{37},\frac{11408}{37}]$ |
$y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$ |
| 930.a.930.1 |
930.a |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.846489\) |
\(0.388226\) |
$[46596,239073,3674852529,119040]$ |
$[11649,5644172,3640360380,2637470125259,930]$ |
$[\frac{71502622649365111083}{310},\frac{1487013548016809538}{155},531176338621566]$ |
$y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$ |
| 953.a.953.1 |
953.a |
\( 953 \) |
\( -953 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006276\) |
\(24.886682\) |
\(0.156194\) |
$[92,1513,26203,121984]$ |
$[23,-41,67,-35,953]$ |
$[\frac{6436343}{953},-\frac{498847}{953},\frac{35443}{953}]$ |
$y^2 + (x^3 + x + 1)y = x^3 + x^2$ |
| 961.a.961.1 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.224644\) |
\(0.449288\) |
$[66980,1011437281,14016353908561,-123008]$ |
$[16745,-30460094,12221475912,-180792178085599,-961]$ |
$[-\frac{1316514841399349215625}{961},\frac{143016680917998700750}{961},-\frac{3426841043882137800}{961}]$ |
$y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$ |
| 961.a.961.2 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.616097\) |
\(0.449288\) |
$[11260,503521,1770579599,123008]$ |
$[2815,309196,43449708,6677190401,961]$ |
$[\frac{176763257309509375}{961},\frac{6897140364776500}{961},\frac{344305262376300}{961}]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$ |
| 961.a.961.3 |
961.a |
\( 31^{2} \) |
\( 31^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.232193\) |
\(0.449288\) |
$[260,1681,185209,123008]$ |
$[65,106,-672,-13729,961]$ |
$[\frac{1160290625}{961},\frac{29110250}{961},-\frac{2839200}{961}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$ |
| 971.a.971.1 |
971.a |
\( 971 \) |
\( -971 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.005970\) |
\(29.647111\) |
\(0.176998\) |
$[256,1024,80304,-3884]$ |
$[128,512,2000,-1536,-971]$ |
$[-\frac{34359738368}{971},-\frac{1073741824}{971},-\frac{32768000}{971}]$ |
$y^2 + y = x^5 - 2x^3 + x$ |
| 997.a.997.1 |
997.a |
\( 997 \) |
\( 997 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.589621\) |
\(0.337338\) |
$[6112,48064,98113399,3988]$ |
$[3056,381120,61964417,11027700988,997]$ |
$[\frac{266542673508171776}{997},\frac{10877317101649920}{997},\frac{578694117523712}{997}]$ |
$y^2 + xy = x^5 - 8x^4 + 16x^3 - x$ |
| 997.a.997.2 |
997.a |
\( 997 \) |
\( 997 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.589621\) |
\(0.337338\) |
$[64,184,391,3988]$ |
$[32,12,305,2404,997]$ |
$[\frac{33554432}{997},\frac{393216}{997},\frac{312320}{997}]$ |
$y^2 + (x + 1)y = x^5 + x^4$ |
| 997.b.997.1 |
997.b |
\( 997 \) |
\( 997 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.081270\) |
\(19.932843\) |
\(0.179992\) |
$[32,16,-1680,-3988]$ |
$[16,8,208,816,-997]$ |
$[-\frac{1048576}{997},-\frac{32768}{997},-\frac{53248}{997}]$ |
$y^2 + y = x^5 - 2x^4 + 2x^3 - x^2$ |
