| 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 |
| 360.a.6480.1 |
360.a |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
| 600.a.18000.1 |
600.a |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(18.934319\) |
\(0.262977\) |
$[1376,23824,11410044,72000]$ |
$[688,15752,244900,-19908576,18000]$ |
$[9634345320448/1125,320612931584/1125,289804864/45]$ |
$y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$ |
| 600.b.450000.1 |
600.b |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{5} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{5} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[18072,38904,233095932,1800000]$ |
$[9036,3395570,1698206400,953774351375,450000]$ |
$[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ |
$y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$ |
| 630.a.34020.1 |
630.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(19.470889\) |
\(0.304233\) |
$[24100,969793,7474503265,4354560]$ |
$[6025,1472118,470090880,166291536519,34020]$ |
$[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$ |
$y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$ |
| 708.a.181248.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{10} \cdot 3 \cdot 59 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.325344\) |
\(0.325344\) |
$[234100,3468879025,202585466081177,-23199744]$ |
$[58525,-1820975,60952909,62829762150,-181248]$ |
$[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$ |
$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$ |
| 816.a.39168.1 |
816.a |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[436,3373,434667,4896]$ |
$[436,5672,77824,439920,39168]$ |
$[61544958196/153,1836351122/153,57789184/153]$ |
$y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$ |
| 936.a.1872.1 |
936.a |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{2} \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(7.131061\) |
\(0.445691\) |
$[45352,11224,169415364,7488]$ |
$[22676,21423170,26983749312,38232821637503,1872]$ |
$[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ |
$y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$ |
| 1050.a.131250.1 |
1050.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 3 \cdot 5^{5} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.612551\) |
\(0.413284\) |
$[11868,198609,759217863,16800000]$ |
$[2967,358520,56735700,9949557875,131250]$ |
$[76641937806559869/43750,312136655012892/4375,475666111026/125]$ |
$y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$ |
| 1344.a.4032.1 |
1344.a |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( - 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.691213\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 - 12x^4 - 48x^2 - 63$ |
| 1470.a.2940.1 |
1470.a |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
\( - 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(8.519256\) |
\(0.532453\) |
$[2556,6897,5825079,376320]$ |
$[639,16726,574080,21769511,2940]$ |
$[35512646315733/980,727349955399/490,3906815328/49]$ |
$y^2 + (x^2 + x)y = -x^6 + 2x^5 - 5x^4 + 4x^3 - 5x^2 + 2x - 1$ |
| 1575.a.23625.1 |
1575.a |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{3} \cdot 7 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.054364\) |
\(17.779771\) |
\(0.241646\) |
$[5748,48105,93031605,3024000]$ |
$[1437,84036,6376864,525376068,23625]$ |
$[226944716565591/875,9235744556604/875,1463114053024/2625]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 6x^3 + 2x^2 + 7x - 4$ |
| 1575.a.165375.1 |
1575.a |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( - 3^{3} \cdot 5^{3} \cdot 7^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.027182\) |
\(17.779771\) |
\(0.241646\) |
$[12,19305,2541195,21168000]$ |
$[3,-804,-34624,-187572,165375]$ |
$[9/6125,-804/6125,-34624/18375]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 2x^4 + x^2 - 2x$ |
| 1584.a.684288.1 |
1584.a |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{5} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(4.753791\) |
\(0.594224\) |
$[7444,76621,183223627,85536]$ |
$[7444,2257800,897608448,396034111728,684288]$ |
$[89287745446261204/2673,1212671977685150/891,1962567037712/27]$ |
$y^2 + (x^3 + x)y = -x^6 + 6x^4 - 17x^2 + 11$ |
| 1680.a.16800.1 |
1680.a |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.090690\) |
\(0.636336\) |
$[404040,44088,5935895700,67200]$ |
$[202020,1700496002,19085068732800,240969733145567999,16800]$ |
$[20029151526577171524000,834544374130868293620,46363176164438078400]$ |
$y^2 + (x^3 + x)y = -x^6 - 18x^4 - 136x^2 - 350$ |
| 1920.a.368640.1 |
1920.a |
\( 2^{7} \cdot 3 \cdot 5 \) |
\( - 2^{13} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.004698\) |
\(0.625587\) |
$[8952,6072,17987052,1440]$ |
$[17904,13340192,13237770240,14762078945024,368640]$ |
$[24952719973569408/5,1038436236963696/5,11510985848256]$ |
$y^2 + (x^3 + x^2 + x + 1)y = 5x^6 + 6x^5 + 17x^4 + 12x^3 + 17x^2 + 6x + 5$ |
| 1935.a.52245.2 |
1935.a |
\( 3^{2} \cdot 5 \cdot 43 \) |
\( - 3^{5} \cdot 5 \cdot 43 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$4$ |
\( 2 \) |
\(1.000000\) |
\(0.234547\) |
\(0.469095\) |
$[307168,3207396712,267640995335223,-208980]$ |
$[153584,448269092,1453877009505,5586766946327864,-52245]$ |
$[-85453503231099874048999424/52245,-1623965199773111994400768/52245,-762091475690810672384/1161]$ |
$y^2 + xy = x^5 - 2x^4 - 82x^3 - 20x^2 + 927x - 1134$ |
| 2058.a.2058.1 |
2058.a |
\( 2 \cdot 3 \cdot 7^{3} \) |
\( 2 \cdot 3 \cdot 7^{3} \) |
$0$ |
$3$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.270.2 |
|
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(3.359562\) |
\(0.839890\) |
$[40908,115154025,1158334769067,-263424]$ |
$[10227,-440104,18634308,-779615725,-2058]$ |
$[-108724120940360583/2,228746634549804,-947031470154]$ |
$y^2 + (x^3 + 1)y = 5x^6 - 4x^5 - 5x^4 + 14x^3 - 5x^2 - 4x + 5$ |
| 2169.a.175689.1 |
2169.a |
\( 3^{2} \cdot 241 \) |
\( 3^{6} \cdot 241 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(10.183530\) |
\(0.636471\) |
$[2860,62145,64270095,92544]$ |
$[2145,168405,12629605,-317435325,175689]$ |
$[186865965446875/723,20518794993125/2169,26790746125/81]$ |
$y^2 + (x^2 + x)y = x^5 - 9x^4 + 22x^3 - 14x^2 - x$ |
| 2304.a.13824.2 |
2304.a |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.90.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.099203\) |
\(11.872466\) |
\(0.294447\) |
$[186,54,2664,54]$ |
$[372,5622,115100,2802579,13824]$ |
$[515324718,83742501/4,27652775/24]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + 3x^2 + x + 2$ |
| 2304.a.13824.1 |
2304.a |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.049602\) |
\(23.744931\) |
\(0.294447\) |
$[102,234,7128,54]$ |
$[204,1110,4324,-87501,13824]$ |
$[25557426,2726715/4,312409/24]$ |
$y^2 + y = 2x^5 + 3x^4 - x^3 - 2x^2$ |
| 2457.a.95823.1 |
2457.a |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( - 3^{4} \cdot 7 \cdot 13^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.066494\) |
\(18.983107\) |
\(0.315567\) |
$[1932,57897,45198315,12265344]$ |
$[483,7308,-43264,-18575844,95823]$ |
$[46360978629/169,1452301788/169,-947968/9]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 3x^3 + 6x^2 - 6x + 2$ |
| 2457.a.154791.1 |
2457.a |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( - 3^{5} \cdot 7^{2} \cdot 13 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.033247\) |
\(18.983107\) |
\(0.315567\) |
$[780,63657,23411115,19813248]$ |
$[195,-1068,-164320,-8295756,154791]$ |
$[89253125/49,-7520500/147,-53404000/1323]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^3 - x^2 + 2$ |
| 2457.b.199017.1 |
2457.b |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( 3^{7} \cdot 7 \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.926544\) |
\(0.620409\) |
$[3308,70369,83658591,104832]$ |
$[2481,230085,22164597,512814483,199017]$ |
$[386836591312907/819,14459801319895/819,2056574503/3]$ |
$y^2 + (x^2 + x)y = -x^5 + 4x^4 + x^3 - 13x^2 - 9x$ |
| 2560.a.5120.1 |
2560.a |
\( 2^{9} \cdot 5 \) |
\( 2^{10} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.45.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(21.001976\) |
\(0.656312\) |
$[80,112,3020,20]$ |
$[160,768,1280,-96256,5120]$ |
$[20480000,614400,6400]$ |
$y^2 = x^5 - x^4 - 2x^3 + x^2 + x$ |
| 2560.a.819200.1 |
2560.a |
\( 2^{9} \cdot 5 \) |
\( 2^{15} \cdot 5^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.45.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(10.500988\) |
\(0.656312\) |
$[484,853,144121,100]$ |
$[1936,147072,13491200,1122197504,819200]$ |
$[829997587232/25,32568377424/25,61726456]$ |
$y^2 = 2x^5 - 7x^4 + 2x^3 + 7x^2 + 2x$ |
| 2600.a.338000.1 |
2600.a |
\( 2^{3} \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 5^{3} \cdot 13^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(6.475715\) |
\(0.809464\) |
$[3608,166936,209750684,1352000]$ |
$[1804,107778,4226816,-997730305,338000]$ |
$[1194160449744064/21125,39547563972312/21125,859738601216/21125]$ |
$y^2 + xy = 10x^5 + 8x^4 - 5x^3 - 3x^2 + x$ |
| 2640.a.2640.1 |
2640.a |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
\( - 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.936322\) |
\(0.867040\) |
$[63768,10392,220729308,10560]$ |
$[31884,42356162,75020763840,149479393726079,2640]$ |
$[686471900571962215488/55,28601826290311163976/55,28888377841215936]$ |
$y^2 + (x^3 + x)y = -x^6 - 10x^4 - 40x^2 - 55$ |
| 2688.a.172032.1 |
2688.a |
\( 2^{7} \cdot 3 \cdot 7 \) |
\( - 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(4.951816\) |
\(0.618977\) |
$[4248,2904,4071996,672]$ |
$[8496,2999840,1408899072,742741622528,172032]$ |
$[1801197437083776/7,74856652932240/7,591152665536]$ |
$y^2 + y = -12x^6 - 36x^5 - 61x^4 - 62x^3 - 42x^2 - 17x - 4$ |
| 2739.a.2739.1 |
2739.a |
\( 3 \cdot 11 \cdot 83 \) |
\( - 3 \cdot 11 \cdot 83 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1, 3.80.2 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.664267\) |
\(0.664267\) |
$[21044,-927505967,-9952421552727,-350592]$ |
$[5261,39799337,82088193169,-288030310344365,-2739]$ |
$[-4030338368178862301/2739,-5795364321847592797/2739,-2272046943202955449/2739]$ |
$y^2 + (x^2 + x + 1)y = 3x^6 + 26x^5 + 40x^4 + 25x^3 + 22x^2 + 7x - 8$ |
| 2745.a.502335.1 |
2745.a |
\( 3^{2} \cdot 5 \cdot 61 \) |
\( - 3^{3} \cdot 5 \cdot 61^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.100418\) |
\(0.693776\) |
$[260,-34487,-4132395,-64298880]$ |
$[65,1613,32085,-129061,-502335]$ |
$[-232058125/100467,-88594025/100467,-3012425/11163]$ |
$y^2 + (x^2 + x)y = 3x^5 + 7x^4 + 5x^3 - x$ |
| 2808.b.454896.1 |
2808.b |
\( 2^{3} \cdot 3^{3} \cdot 13 \) |
\( 2^{4} \cdot 3^{7} \cdot 13 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.282584\) |
\(11.387805\) |
\(0.402251\) |
$[45352,11224,169415364,7488]$ |
$[68028,192808530,728561231424,3096858552637743,454896]$ |
$[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ |
$y^2 + (x^3 + x)y = -9x^4 + 95x^2 - 351$ |
| 2872.a.367616.1 |
2872.a |
\( 2^{3} \cdot 359 \) |
\( - 2^{10} \cdot 359 \) |
$1$ |
$3$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 2 \) |
\(0.379949\) |
\(4.123656\) |
\(0.391695\) |
$[52152,30585,530058255,45952]$ |
$[52152,113305906,328168275184,1069100888228783,367616]$ |
$[376751407549293075168/359,15695150888732498127/359,871642853702611839/359]$ |
$y^2 + xy = -8x^6 - 28x^5 - 65x^4 - 88x^3 - 88x^2 - 51x - 20$ |
| 2880.e.43200.1 |
2880.e |
\( 2^{6} \cdot 3^{2} \cdot 5 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.351604\) |
\(4.640585\) |
\(0.392014\) |
$[518864,13453,2326627806,5400]$ |
$[518864,11217484802,323352207187200,10485963586719590399,43200]$ |
$[587608031126100483000713216/675,24483648388282979553688192/675,2015111872140962978816]$ |
$y^2 + xy = 3x^6 + 38x^4 + 160x^2 + 225$ |
| 2898.a.8694.1 |
2898.a |
\( 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
\( 2 \cdot 3^{3} \cdot 7 \cdot 23 \) |
$0$ |
$3$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$4$ |
\( 3 \) |
\(1.000000\) |
\(1.380505\) |
\(0.460168\) |
$[82604,1039610905,17451947366819,-1112832]$ |
$[20651,-25547796,26482045716,-26452288594125,-8694]$ |
$[-3755825735457104328251/8694,12499832534439302222/483,-1299014708339214]$ |
$y^2 + (x^3 + 1)y = -10x^6 + 18x^5 - 23x^4 + 36x^3 - 23x^2 + 18x - 10$ |
| 2976.a.761856.1 |
2976.a |
\( 2^{5} \cdot 3 \cdot 31 \) |
\( - 2^{13} \cdot 3 \cdot 31 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.756854\) |
\(0.756854\) |
$[5144,1850140,2332652300,-2976]$ |
$[10288,-523584,32317696,14586062848,-761856]$ |
$[-14069051982264704/93,23198934303648/31,-417553721672/93]$ |
$y^2 + y = -4x^6 - 20x^5 - 19x^4 + 18x^3 + 5x^2 - 3x - 1$ |
| 3003.b.819819.1 |
3003.b |
\( 3 \cdot 7 \cdot 11 \cdot 13 \) |
\( - 3^{2} \cdot 7^{2} \cdot 11 \cdot 13^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.060530\) |
\(13.204144\) |
\(0.399621\) |
$[240,-60,-206121,-3279276]$ |
$[120,610,26569,704045,-819819]$ |
$[-2764800000/91091,-117120000/91091,-42510400/91091]$ |
$y^2 + (x^2 + 1)y = x^5 + 4x^4 + 3x^3 + x$ |
| 3030.a.90900.1 |
3030.a |
\( 2 \cdot 3 \cdot 5 \cdot 101 \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 101 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.045211\) |
\(18.504176\) |
\(0.418298\) |
$[6912,670992,1363312431,363600]$ |
$[3456,385832,51431049,7219843280,90900]$ |
$[13695130288521216/2525,442401860616192/2525,17063587713024/2525]$ |
$y^2 + xy = 5x^5 + 28x^4 + 52x^3 + 33x^2 + 2x$ |
| 3072.b.196608.2 |
3072.b |
\( 2^{10} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.143062\) |
\(0.767883\) |
$[2376,321,254043,24]$ |
$[9504,3760160,1981759488,1173959737088,196608]$ |
$[394394593494528,16418157695280,910463659776]$ |
$y^2 = 2x^6 + 9x^4 + 13x^2 + 6$ |
| 3080.a.67760.1 |
3080.a |
\( 2^{3} \cdot 5 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 5 \cdot 7 \cdot 11^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.121981\) |
\(13.601857\) |
\(0.414790\) |
$[64,-6176,-164068,-271040]$ |
$[32,1072,9156,-214048,-67760]$ |
$[-2097152/4235,-2195456/4235,-83712/605]$ |
$y^2 + (x + 1)y = 2x^5 - 2x^4 - x^2$ |
| 3120.b.199680.1 |
3120.b |
\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
\( - 2^{10} \cdot 3 \cdot 5 \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.338010\) |
\(0.834502\) |
$[2397240,72897,58245771285,24960]$ |
$[2397240,239448268802,31889707498721280,4777952242989938687999,199680]$ |
$[5154260479603163815124340000/13,214760809729321817508682425/13,917780865738818887929600]$ |
$y^2 + xy = -80x^6 - 189x^4 - 149x^2 - 39$ |
| 3150.b.78750.1 |
3150.b |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 3^{2} \cdot 5^{4} \cdot 7 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.532647\) |
\(20.082418\) |
\(0.334276\) |
$[3980,266089,400578411,10080000]$ |
$[995,30164,-218988,-281939989,78750]$ |
$[1560398004995/126,118855194118/315,-68826538/25]$ |
$y^2 + (x^3 + 1)y = -4x^4 + 5x^3 + 14x^2 - 39x + 26$ |
| 3168.a.684288.1 |
3168.a |
\( 2^{5} \cdot 3^{2} \cdot 11 \) |
\( - 2^{8} \cdot 3^{5} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
|
|
$2$ |
\( 2^{3} \) |
\(1.000000\) |
\(3.716043\) |
\(0.929011\) |
$[7444,76621,183223627,85536]$ |
$[7444,2257800,897608448,396034111728,684288]$ |
$[89287745446261204/2673,1212671977685150/891,1962567037712/27]$ |
$y^2 + (x^3 + x)y = -x^6 - 7x^4 - 17x^2 - 11$ |
| 3200.f.819200.1 |
3200.f |
\( 2^{7} \cdot 5^{2} \) |
\( 2^{15} \cdot 5^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.717386\) |
\(15.397662\) |
\(0.460253\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = x^6 - 5x^4 + 7x^2 - 2$ |
| 3219.a.280053.1 |
3219.a |
\( 3 \cdot 29 \cdot 37 \) |
\( 3^{2} \cdot 29^{2} \cdot 37 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.193324\) |
\(8.824733\) |
\(0.426509\) |
$[3656,28648,33859075,1120212]$ |
$[1828,134458,12802201,1330867416,280053]$ |
$[20411783673914368/280053,22197982115968/7569,42779630026384/280053]$ |
$y^2 + (x^3 + x^2)y = -3x^4 - 5x^3 + 6x^2 + 7x - 6$ |
| 3336.b.20016.1 |
3336.b |
\( 2^{3} \cdot 3 \cdot 139 \) |
\( - 2^{4} \cdot 3^{2} \cdot 139 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.111345\) |
\(15.794827\) |
\(0.439668\) |
$[136,-728,-8748,80064]$ |
$[68,314,-592,-34713,20016]$ |
$[90870848/1251,6170728/1251,-171088/1251]$ |
$y^2 + (x^2 + 1)y = x^5 - x^4 - x$ |
| 3360.b.241920.1 |
3360.b |
\( 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.720.4 |
|
|
$2$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(3.848391\) |
\(0.641398\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[5832248478791381977500/7,243004434356588125950/7,1928513067842084400]$ |
$y^2 + (x^2 + 1)y = -135x^6 - 96x^4 - 23x^2 - 2$ |
| 3417.a.686817.1 |
3417.a |
\( 3 \cdot 17 \cdot 67 \) |
\( 3^{2} \cdot 17 \cdot 67^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.580296\) |
\(0.723769\) |
$[1348,46057,19365765,87912576]$ |
$[337,2813,-731,-2039829,686817]$ |
$[4346598285457/686817,107661254189/686817,-4883467/40401]$ |
$y^2 + (x^2 + x)y = 3x^5 - 9x^4 + 6x^3 - x$ |
| 3429.a.30861.1 |
3429.a |
\( 3^{3} \cdot 127 \) |
\( 3^{5} \cdot 127 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.105723\) |
\(16.844197\) |
\(0.445207\) |
$[1552,6068,3179741,508]$ |
$[2328,216714,25552273,3130183437,30861]$ |
$[281389965541376/127,33755992153088/381,121157209024/27]$ |
$y^2 + xy = x^5 + x^4 - 8x^3 - 9x^2 + 16x + 19$ |
| 3465.a.800415.1 |
3465.a |
\( 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
\( - 3^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.079548\) |
\(9.804871\) |
\(0.389980\) |
$[468,-60903,-7272387,-102453120]$ |
$[117,3108,22240,-1764396,-800415]$ |
$[-812017791/29645,-26337636/4235,-2255136/5929]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^3 - 3x^2 + 3x + 2$ |
| 3515.a.333925.1 |
3515.a |
\( 5 \cdot 19 \cdot 37 \) |
\( 5^{2} \cdot 19^{2} \cdot 37 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.098009\) |
\(18.392505\) |
\(0.450657\) |
$[1144,47884,15303367,1335700]$ |
$[572,5652,881,-7860293,333925]$ |
$[61232239557632/333925,1057767549696/333925,288249104/333925]$ |
$y^2 + (x^2 + 1)y = x^5 - 6x^3 + 2x^2 + 2x$ |
