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