| 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 |
| 169.a.169.1 |
169.a |
\( 13^{2} \) |
\( - 13^{2} \) |
$0$ |
$0$ |
$\Z/19\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 277.a.277.1 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.205749\) |
\(0.143137\) |
$[64,352,9552,-1108]$ |
$[32,-16,-464,-3776,-277]$ |
$[-33554432/277,524288/277,475136/277]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$ |
| 277.a.277.2 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.578417\) |
\(0.143137\) |
$[4480,1370512,1511819744,-1108]$ |
$[2240,-19352,164384,-1569936,-277]$ |
$[-56394933862400000/277,217505333248000/277,-824813158400/277]$ |
$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 349.a.349.1 |
349.a |
\( 349 \) |
\( 349 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.988484\) |
\(0.165612\) |
$[8,208,1464,-1396]$ |
$[4,-34,-124,-413,-349]$ |
$[-1024/349,2176/349,1984/349]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$ |
| 353.a.353.1 |
353.a |
\( 353 \) |
\( -353 \) |
$0$ |
$0$ |
$\Z/11\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.495495\) |
\(0.185913\) |
$[188,817,30871,45184]$ |
$[47,58,256,2167,353]$ |
$[229345007/353,6021734/353,565504/353]$ |
$y^2 + (x^3 + x + 1)y = x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(29.135501\) |
\(0.198201\) |
$[36,1569,-13743,99328]$ |
$[9,-62,356,-160,776]$ |
$[59049/776,-22599/388,7209/194]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$ |
| 461.a.461.1 |
461.a |
\( 461 \) |
\( 461 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.048435\) |
\(0.245886\) |
$[1176,144,66456,1844]$ |
$[588,14382,467132,16957923,461]$ |
$[70288881159168/461,2923824242304/461,161508086208/461]$ |
$y^2 + x^3y = x^5 - 3x^3 + 3x - 2$ |
| 461.a.461.2 |
461.a |
\( 461 \) |
\( 461 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.245886\) |
\(0.245886\) |
$[80664,166117104,3752725952952,1844]$ |
$[40332,40091742,45075737276,52661714805267,461]$ |
$[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$ |
$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$ |
| 484.a.1936.1 |
484.a |
\( 2^{2} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.060256\) |
\(0.248432\) |
$[284,2401,246639,-67712]$ |
$[71,110,-624,-14101,-529]$ |
$[-1804229351/529,-39370210/529,3145584/529]$ |
$y^2 + (x^3 + x + 1)y = -x^5$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.411617\) |
\(0.294115\) |
$[120,192,9912,2388]$ |
$[60,118,-68,-4501,597]$ |
$[259200000/199,8496000/199,-81600/199]$ |
$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$ |
| 604.a.9664.1 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.291788\) |
\(0.291788\) |
$[49556,-797087975,-23996873337603,1236992]$ |
$[12389,39607304,223396249616,299729401586052,9664]$ |
$[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$ |
| 604.a.9664.2 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\Z/27\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(23.634831\) |
\(0.291788\) |
$[116,6265,95277,1236992]$ |
$[29,-226,836,-6708,9664]$ |
$[20511149/9664,-2755957/4832,175769/2416]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$ |
| 676.a.5408.1 |
676.a |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{5} \cdot 13^{2} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.60.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(20.169780\) |
\(0.320155\) |
$[204,3273,161211,692224]$ |
$[51,-28,0,-196,5408]$ |
$[345025251/5408,-928557/1352,0]$ |
$y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$ |
| 676.a.562432.1 |
676.a |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(1.000000\) |
\(6.723260\) |
\(0.320155\) |
$[1620,52953,29527389,71991296]$ |
$[405,4628,-8112,-6175936,562432]$ |
$[10896201253125/562432,5912281125/10816,-492075/208]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$ |
| 676.b.17576.1 |
676.b |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$0$ |
$0$ |
2.120.4, 3.17280.1 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[2909390022551/17576,4602275343/676,10349147/26]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.149881\) |
\(0.285801\) |
$[92,73,6379,-91264]$ |
$[23,19,-41,-326,-713]$ |
$[-279841/31,-10051/31,943/31]$ |
$y^2 + (x^3 + x + 1)y = -x^4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.572840\) |
\(0.303368\) |
$[124,1417,38763,95360]$ |
$[31,-19,39,212,745]$ |
$[28629151/745,-566029/745,37479/745]$ |
$y^2 + (x^3 + x + 1)y = -x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.440989\) |
\(0.355939\) |
$[24,528,7608,3188]$ |
$[12,-82,-548,-3325,797]$ |
$[248832/797,-141696/797,-78912/797]$ |
$y^2 + y = x^5 - x^4 + x^3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.284557\) |
\(0.291522\) |
$[1420,4201,1973899,107648]$ |
$[355,5076,93408,1848516,841]$ |
$[5638216721875/841,227094529500/841,11771743200/841]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.488991\) |
\(0.339370\) |
$[552,696,112755,3448]$ |
$[276,3058,45033,769436,862]$ |
$[800784050688/431,32146576704/431,1715216904/431]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$ |
| 886.a.3544.1 |
886.a |
\( 2 \cdot 443 \) |
\( 2^{3} \cdot 443 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(24.085472\) |
\(0.321140\) |
$[232,1180,93881,-14176]$ |
$[116,364,-481,-47073,-3544]$ |
$[-2625427072/443,-71020768/443,809042/443]$ |
$y^2 + (x^3 + x)y = -x^4 - x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.232193\) |
\(0.449288\) |
$[260,1681,185209,123008]$ |
$[65,106,-672,-13729,961]$ |
$[1160290625/961,29110250/961,-2839200/961]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$ |
| 961.a.923521.1 |
961.a |
\( 31^{2} \) |
\( 31^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(2.246439\) |
\(0.449288\) |
$[4100,78961,94151689,118210688]$ |
$[1025,40486,2121888,133954751,923521]$ |
$[1131408212890625/923521,1406419156250/29791,2319780000/961]$ |
$y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$ |
| 976.a.999424.1 |
976.a |
\( 2^{4} \cdot 61 \) |
\( 2^{14} \cdot 61 \) |
$0$ |
$0$ |
$\Z/29\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,29$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 29 \) |
\(1.000000\) |
\(12.900365\) |
\(0.444840\) |
$[152,1012,68714,-124928]$ |
$[152,288,-24464,-950368,-999424]$ |
$[-4952198/61,-61731/61,551969/976]$ |
$y^2 + (x + 1)y = x^6 - 2x^5 + 2x^3 - x^2$ |
| 1012.a.4048.1 |
1012.a |
\( 2^{2} \cdot 11 \cdot 23 \) |
\( 2^{4} \cdot 11 \cdot 23 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(18.518969\) |
\(0.411533\) |
$[140,2425,78163,-518144]$ |
$[35,-50,-4,-660,-4048]$ |
$[-52521875/4048,1071875/2024,1225/1012]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + x$ |
| 1042.a.1042.1 |
1042.a |
\( 2 \cdot 521 \) |
\( 2 \cdot 521 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.423017\) |
\(0.375593\) |
$[480,3912,728889,-4168]$ |
$[240,1748,-5521,-1095136,-1042]$ |
$[-398131200000/521,-12082176000/521,159004800/521]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$ |
| 1069.a.1069.1 |
1069.a |
\( 1069 \) |
\( 1069 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.937046\) |
\(0.304838\) |
$[244,3193,263789,136832]$ |
$[61,22,-884,-13602,1069]$ |
$[844596301/1069,4993582/1069,-3289364/1069]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^3$ |
| 1077.b.1077.1 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.157286\) |
\(0.406291\) |
$[320,544,55360,4308]$ |
$[160,976,7360,56256,1077]$ |
$[104857600000/1077,3997696000/1077,188416000/1077]$ |
$y^2 + x^3y = x^5 + x^4 - x - 2$ |
| 1077.b.1077.2 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.406291\) |
\(0.406291\) |
$[107840,22281904,765878465200,4308]$ |
$[53920,117426616,333407026000,1047074174177136,1077]$ |
$[455773864377135923200000/1077,18408406506675601408000/1077,969336384916326400000/1077]$ |
$y^2 + y = x^5 + 14x^4 + 38x^3 - 79x^2 + 15x - 1$ |
| 1109.a.1109.1 |
1109.a |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.288506\) |
\(0.288506\) |
$[38880,87301728,855606760992,4436]$ |
$[19440,1196112,510249312,2122140677184,1109]$ |
$[2776395315422822400000/1109,8787404722987008000/1109,192830154395443200/1109]$ |
$y^2 + y = x^5 - 6x^4 - 36x^3 - 6x^2 + 63x - 36$ |
| 1109.b.1109.1 |
1109.b |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.606017\) |
\(0.440939\) |
$[248,-32,-10424,4436]$ |
$[124,646,5388,62699,1109]$ |
$[29316250624/1109,1231679104/1109,82845888/1109]$ |
$y^2 + y = x^5 - x^4 - x^3 + x^2 + x$ |
| 1109.c.1109.1 |
1109.c |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.552149\) |
\(0.382086\) |
$[392,292,36703,4436]$ |
$[196,1552,16001,181873,1109]$ |
$[289254654976/1109,11685839872/1109,614694416/1109]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - 2x^2 - 1$ |
| 1116.a.214272.1 |
1116.a |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( - 2^{8} \cdot 3^{3} \cdot 31 \) |
$0$ |
$0$ |
$\Z/39\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \cdot 13 \) |
\(1.000000\) |
\(16.984099\) |
\(0.435490\) |
$[52,22201,238285,-27426816]$ |
$[13,-918,36,-210564,-214272]$ |
$[-371293/214272,37349/3968,-169/5952]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$ |
| 1164.a.1164.1 |
1164.a |
\( 2^{2} \cdot 3 \cdot 97 \) |
\( 2^{2} \cdot 3 \cdot 97 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.402119\) |
\(0.456085\) |
$[500,-47,46665,148992]$ |
$[125,653,3805,12304,1164]$ |
$[30517578125/1164,1275390625/1164,59453125/1164]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 - 1$ |
| 1164.b.670464.1 |
1164.b |
\( 2^{2} \cdot 3 \cdot 97 \) |
\( 2^{8} \cdot 3^{3} \cdot 97 \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(1.000000\) |
\(8.941486\) |
\(0.425785\) |
$[372,4521,1271253,85819392]$ |
$[93,172,-10928,-261472,670464]$ |
$[257662359/24832,1281013/6208,-656363/4656]$ |
$y^2 + (x^2 + x + 1)y = 2x^5 - 2x^4 + x^3 - x^2$ |
| 1210.a.1210.1 |
1210.a |
\( 2 \cdot 5 \cdot 11^{2} \) |
\( 2 \cdot 5 \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.20.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.627716\) |
\(0.345109\) |
$[208,75964,-1718663,-4840]$ |
$[104,-12210,559319,-22728731,-1210]$ |
$[-6083264512/605,124859904/11,-3024797152/605]$ |
$y^2 + (x^3 + x)y = 3x^3 - 2x^2 + 6x + 2$ |
| 1231.a.1231.1 |
1231.a |
\( 1231 \) |
\( 1231 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(16.048501\) |
\(0.327520\) |
$[1108,361,95637,157568]$ |
$[277,3182,49028,863908,1231]$ |
$[1630793025157/1231,67630014806/1231,3761869412/1231]$ |
$y^2 + (x^3 + 1)y = -x^4 + 2x^2 - x - 2$ |
| 1285.a.1285.1 |
1285.a |
\( 5 \cdot 257 \) |
\( 5 \cdot 257 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.221343\) |
\(0.494313\) |
$[56,-1376,-87560,5140]$ |
$[28,262,7996,38811,1285]$ |
$[17210368/1285,5751424/1285,6268864/1285]$ |
$y^2 + y = x^5 - 2x^4 + 3x^3 - x$ |
| 1444.a.46208.1 |
1444.a |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{7} \cdot 19^{2} \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(23.233383\) |
\(0.516297\) |
$[788,37225,7245653,5914624]$ |
$[197,66,1940,94456,46208]$ |
$[296709280757/46208,252297309/23104,18822365/11552]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^3 + x$ |
| 1444.b.109744.1 |
1444.b |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{3} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.60.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(1.509904\) |
\(0.503301\) |
$[4328,28957,40080803,13718]$ |
$[4328,761178,175243840,44765847959,109744]$ |
$[94910940689819648/6859,202989886275264/361,568316258560/19]$ |
$y^2 + x^3y = -4x^4 + 16x^2 - 19$ |
| 1468.b.5872.1 |
1468.b |
\( 2^{2} \cdot 367 \) |
\( 2^{4} \cdot 367 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(22.526896\) |
\(0.500598\) |
$[140,169,346155,-751616]$ |
$[35,44,-4640,-41084,-5872]$ |
$[-52521875/5872,-471625/1468,355250/367]$ |
$y^2 + (x^2 + x + 1)y = -2x^5 - 2x^4$ |
| 1532.a.1532.1 |
1532.a |
\( 2^{2} \cdot 383 \) |
\( 2^{2} \cdot 383 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.961311\) |
\(0.518452\) |
$[372,2673,322425,196096]$ |
$[93,249,261,-9432,1532]$ |
$[6956883693/1532,200284893/1532,2257389/1532]$ |
$y^2 + (x^3 + 1)y = -x - 1$ |
| 1532.a.392192.1 |
1532.a |
\( 2^{2} \cdot 383 \) |
\( 2^{10} \cdot 383 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.518452\) |
\(0.518452\) |
$[52500,33335793,517241464281,50200576]$ |
$[13125,5788743,3113886477,1840053622644,392192]$ |
$[389490222930908203125/392192,13088268780029296875/392192,536415600139453125/392192]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 7x^4 - 53x^2 + 12x - 1$ |
| 1589.a.1589.1 |
1589.a |
\( 7 \cdot 227 \) |
\( 7 \cdot 227 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.424681\) |
\(0.536987\) |
$[480,1872,427680,6356]$ |
$[240,2088,5280,-773136,1589]$ |
$[796262400000/1589,28864512000/1589,304128000/1589]$ |
$y^2 + y = x^5 + 4x^4 + 4x^3 - x^2 - x$ |
| 1665.a.1665.1 |
1665.a |
\( 3^{2} \cdot 5 \cdot 37 \) |
\( - 3^{2} \cdot 5 \cdot 37 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(16.175945\) |
\(0.647038\) |
$[572,1969,296919,213120]$ |
$[143,770,5904,62843,1665]$ |
$[59797108943/1665,450327878/333,13414544/185]$ |
$y^2 + (x^3 + x^2 + 1)y = x^4 + x^3 + 2x^2 + 2x + 1$ |
| 1696.b.434176.1 |
1696.b |
\( 2^{5} \cdot 53 \) |
\( - 2^{13} \cdot 53 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1, 3.2880.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.985343\) |
\(0.665038\) |
$[11236,7908289,22291799553,54272]$ |
$[11236,-11872,-76224768,-214150609408,434176]$ |
$[3299763591802133/8,-155150527903/4,-44328573381/2]$ |
$y^2 + xy = x^6 - 2x^5 + 2x^4 + 9x^3 - 12x^2 + 3x + 26$ |
| 1701.a.1701.1 |
1701.a |
\( 3^{5} \cdot 7 \) |
\( 3^{5} \cdot 7 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.723792\) |
\(0.723792\) |
$[84128,228576,6363290016,28]$ |
$[126192,663174672,4644628928416,36578592038091072,1701]$ |
$[131690013992224449101824/7,16452745612696372576256/21,8218113979245079207936/189]$ |
$y^2 + y = x^5 + 19x^4 + 86x^3 - 60x^2 + 12x - 1$ |
| 1811.b.1811.1 |
1811.b |
\( 1811 \) |
\( -1811 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(28.759955\) |
\(0.586938\) |
$[424,2608,429128,7244]$ |
$[212,1438,-28,-518445,1811]$ |
$[428232184832/1811,13701448064/1811,-1258432/1811]$ |
$y^2 + x^3y = x^5 + x^4 - x^3 - 3x^2 - x + 2$ |
