| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 294.a.294.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( - 2 \cdot 3 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.451533\) |
\(0.148969\) |
$[236,505,18451,37632]$ |
$[59,124,564,4475,294]$ |
$[714924299/294,12733498/147,327214/49]$ |
$y^2 + (x^3 + 1)y = x^4 + x^2$ |
| 294.a.8232.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{3} \cdot 3 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[25353016669288549/8232,75211396489919/588,49431027484/7]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 336.a.172032.1 |
336.a |
\( 2^{4} \cdot 3 \cdot 7 \) |
\( - 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.356066\) |
\(0.178033\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
| 363.a.11979.1 |
363.a |
\( 3 \cdot 11^{2} \) |
\( - 3^{2} \cdot 11^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.970596\) |
\(0.189706\) |
$[344,-3068,-526433,-47916]$ |
$[172,1744,45841,1210779,-11979]$ |
$[-150536645632/11979,-8874253312/11979,-1356160144/11979]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$ |
| 363.a.43923.1 |
363.a |
\( 3 \cdot 11^{2} \) |
\( - 3 \cdot 11^{4} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.794119\) |
\(0.189706\) |
$[11096,25612,88274095,-175692]$ |
$[5548,1278244,392069161,135322995423,-43923]$ |
$[-5256325630316243968/43923,-1804005053317888/363,-99735603013264/363]$ |
$y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$ |
| 448.a.448.2 |
448.a |
\( 2^{6} \cdot 7 \) |
\( - 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
| 448.a.448.1 |
448.a |
\( 2^{6} \cdot 7 \) |
\( 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.792789\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = x^4 - 7$ |
| 450.a.2700.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[364,3529,393211,345600]$ |
$[91,198,0,-9801,2700]$ |
$[6240321451/2700,8289281/150,0]$ |
$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$ |
| 450.a.36450.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[23444,212089,1627179821,4665600]$ |
$[5861,1422468,457836300,164990835819,36450]$ |
$[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(26.722339\) |
\(0.247429\) |
$[7340,1042345,2905273355,121856]$ |
$[1835,96870,-3910340,-4139817700,952]$ |
$[20805604708146875/952,299272981175625/476,-27661753375/2]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |
| 504.a.27216.1 |
504.a |
\( 2^{3} \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{5} \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.782699\) |
\(0.243209\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[12063042849801664/243,167186257609000/81,3083035208512/27]$ |
$y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.396252\) |
\(0.223963\) |
$[68,124,2616,72]$ |
$[68,110,-36,-3637,576]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$ |
| 578.a.2312.1 |
578.a |
\( 2 \cdot 17^{2} \) |
\( 2^{3} \cdot 17^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(13.910299\) |
\(0.289798\) |
$[228,705,135777,295936]$ |
$[57,106,-992,-16945,2312]$ |
$[601692057/2312,9815229/1156,-402876/289]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$ |
| 588.a.18816.1 |
588.a |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{7} \cdot 3 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(20.658150\) |
\(0.286919\) |
$[748,11545,2902787,2408448]$ |
$[187,976,-192,-247120,18816]$ |
$[228669389707/18816,398891383/1176,-34969/98]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$ |
| 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.a.96000.1 |
600.a |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3 \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.467159\) |
\(0.262977\) |
$[92,4981,43947,-12000]$ |
$[92,-2968,47600,-1107456,-96000]$ |
$[-25745372/375,9027914/375,-62951/15]$ |
$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$ |
| 600.b.30000.1 |
600.b |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3 \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[600,18744,4690524,120000]$ |
$[300,626,-198336,-14973169,30000]$ |
$[81000000,563400,-595008]$ |
$y^2 + (x^3 + x)y = x^4 + x^2 - 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(19.470889\) |
\(0.304233\) |
$[24100,969793,7474503265,4354560]$ |
$[6025,1472118,470090880,166291536519,34020]$ |
$[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$ |
$y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$ |
| 640.a.81920.1 |
640.a |
\( 2^{7} \cdot 5 \) |
\( - 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = 3x^4 + 13x^2 + 20$ |
| 640.a.81920.2 |
640.a |
\( 2^{7} \cdot 5 \) |
\( 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = -3x^4 + 13x^2 - 20$ |
| 644.a.2576.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{4} \cdot 7 \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(3.928431\) |
\(0.218246\) |
$[39036,4124865,50880984159,329728]$ |
$[9759,3796384,1910683600,1058457444236,2576]$ |
$[88516980336138032799/2576,220529201888022246/161,70640465629725]$ |
$y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$ |
| 644.a.659456.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 7 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.872985\) |
\(0.218246\) |
$[161796,1070662305,46065265919409,84410368]$ |
$[40449,23560804,14638854160,9253881697856,659456]$ |
$[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ |
$y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$ |
| 672.a.172032.1 |
672.a |
\( 2^{5} \cdot 3 \cdot 7 \) |
\( 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(1.113349\) |
\(0.278337\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(1.000000\) |
\(6.723260\) |
\(0.320155\) |
$[1620,52953,29527389,71991296]$ |
$[405,4628,-8112,-6175936,562432]$ |
$[10896201253125/562432,5912281125/10816,-492075/208]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.491655\) |
\(0.319213\) |
$[420,4305,640185,87808]$ |
$[105,280,-980,-45325,686]$ |
$[37209375/2,472500,-15750]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$ |
| 720.a.6480.1 |
720.a |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.444268\) |
\(0.295133\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$ |
| 720.b.116640.1 |
720.b |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{5} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(14.457058\) |
\(0.301189\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ |
$y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$ |
| 726.a.1452.1 |
726.a |
\( 2 \cdot 3 \cdot 11^{2} \) |
\( - 2^{2} \cdot 3 \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.124086\) |
\(0.302482\) |
$[760,-69236,-16142609,-5808]$ |
$[380,17556,702601,-10306189,-1452]$ |
$[-1980879200000/363,-7297976000/11,-25363896100/363]$ |
$y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$ |
| 784.a.1568.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{5} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(20.793351\) |
\(0.288797\) |
$[792,120,15228,6272]$ |
$[396,6514,144256,3673295,1568]$ |
$[304316815968/49,12641055372/49,14427072]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$ |
| 784.a.43904.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{7} \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(6.931117\) |
\(0.288797\) |
$[21288,3000,20891172,175616]$ |
$[10644,4720114,2790613504,1855953490895,43904]$ |
$[1067368445729034408/343,6352710665144931/49,50408453477952/7]$ |
$y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$ |
| 784.b.12544.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.270100\) |
\(0.313058\) |
$[116,445,16259,1568]$ |
$[116,264,-1280,-54544,12544]$ |
$[82044596/49,1609674/49,-67280/49]$ |
$y^2 + (x^3 + x)y = -1$ |
| 784.b.25088.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.626117\) |
\(0.313058\) |
$[2740,15382525,36170522453,3136]$ |
$[2740,-9942200,-24298750736,-41356479464160,25088]$ |
$[301635777856250/49,-399451653071875/49,-712598832131225/98]$ |
$y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$ |
| 784.b.76832.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{5} \cdot 7^{4} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.2160.20 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(3.756700\) |
\(0.313058\) |
$[1520,132280,50979316,307328]$ |
$[760,2020,6076,134340,76832]$ |
$[7923516800000/2401,27710360000/2401,2238200/49]$ |
$y^2 + (x + 1)y = -x^6 + 4x^5 - 4x^4 - 2x^3 + 10x - 9$ |
| 784.c.614656.1 |
784.c |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.5760.7 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.731485\) |
\(0.358218\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[1248318403996/2401,9291226221/4802,-23245787/9604]$ |
$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$ |
| 800.a.1600.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[0,84,936,200]$ |
$[0,-56,832,-784,-1600]$ |
$[0,-134456/625,728/25]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$ |
| 800.a.8000.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.4, 3.720.5 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.590050\) |
\(0.349378\) |
$[192,11604,322392,-1000]$ |
$[192,-6200,142400,-2774800,-8000]$ |
$[-4076863488/125,27426816/5,-3280896/5]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$ |
| 800.a.409600.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 + 1$ |
| 810.a.196830.1 |
810.a |
\( 2 \cdot 3^{4} \cdot 5 \) |
\( - 2 \cdot 3^{9} \cdot 5 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.640.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(0.328982\) |
\(0.328982\) |
$[103200,92148840,2874875039973,-3240]$ |
$[154800,860236740,5905731060081,43549979813677800,-196830]$ |
$[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$ |
$y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$ |
| 816.b.52224.1 |
816.b |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{10} \cdot 3 \cdot 17 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(2.423742\) |
\(0.403957\) |
$[15964,2380825,11444690699,6528]$ |
$[15964,9031504,6282991104,4683401370560,52224]$ |
$[1012531723491160951/51,35882713644370099/51,30660536527816]$ |
$y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$ |
| 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.b.9317.1 |
847.b |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.827271\) |
\(0.336545\) |
$[304,5932,452465,-37268]$ |
$[152,-26,-401,-15407,-9317]$ |
$[-81136812032/9317,91307008/9317,9264704/9317]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x$ |
