| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.792789\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = x^4 - 7$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = -3x^4 + 13x^2 - 20$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.491655\) |
\(0.319213\) |
$[420,4305,640185,87808]$ |
$[105,280,-980,-45325,686]$ |
$[37209375/2,472500,-15750]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(0.328982\) |
\(0.328982\) |
$[103200,92148840,2874875039973,-3240]$ |
$[154800,860236740,5905731060081,43549979813677800,-196830]$ |
$[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$ |
$y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$ |
| 864.a.1728.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(18.142966\) |
\(0.377978\) |
$[96,180,5256,216]$ |
$[96,264,576,-3600,1728]$ |
$[4718592,135168,3072]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$ |
| 864.a.221184.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{13} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(18.142966\) |
\(0.377978\) |
$[168,34560,-211428,-864]$ |
$[336,-87456,10192896,-1055934720,-221184]$ |
$[-19361664,14998704,-5202624]$ |
$y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$ |
| 864.a.442368.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(9.071483\) |
\(0.377978\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 - 4x^4 + 6x^2 - 3$ |
| 1088.b.2176.1 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.893944\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = 4x^4 + 24x^2 + 34$ |
| 1088.b.2176.2 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.575776\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = -5x^4 + 24x^2 - 34$ |
| 1331.a.1331.1 |
1331.a |
\( 11^{3} \) |
\( - 11^{3} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.30.4, 3.540.8 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.179570\) |
\(30.476389\) |
\(0.218906\) |
$[88,2068,83248,5324]$ |
$[44,-264,-4840,-70664,1331]$ |
$[123904,-16896,-7040]$ |
$y^2 + x^3y = -x^4 - x^3 + 2x^2 + 3x + 1$ |
| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.691213\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 - 12x^4 - 48x^2 - 63$ |
| 1344.a.4032.2 |
1344.a |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.382426\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 + 12x^4 - 48x^2 + 63$ |
| 1536.b.49152.2 |
1536.b |
\( 2^{9} \cdot 3 \) |
\( - 2^{14} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.996682\) |
\(0.499793\) |
$[624,141,29202,6]$ |
$[2496,258080,35377152,5424021248,49152]$ |
$[1970977701888,81648253440,4484054016]$ |
$y^2 + x^3y = 3x^4 + 11x^2 + 12$ |
| 1536.b.49152.1 |
1536.b |
\( 2^{9} \cdot 3 \) |
\( 2^{14} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(15.993364\) |
\(0.499793\) |
$[624,141,29202,6]$ |
$[2496,258080,35377152,5424021248,49152]$ |
$[1970977701888,81648253440,4484054016]$ |
$y^2 + x^3y = -3x^4 + 11x^2 - 12$ |
| 1536.c.98304.1 |
1536.c |
\( 2^{9} \cdot 3 \) |
\( 2^{15} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.680538\) |
\(0.552517\) |
$[1068,38019,11064156,12]$ |
$[4272,354880,32280576,2990701568,98304]$ |
$[14473882091808,281451823560,5992838496]$ |
$y^2 + y = 4x^6 - 12x^5 + 3x^4 + 14x^3 - 5x^2 - 4x + 1$ |
| 1728.b.442368.1 |
1728.b |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.091187\) |
\(0.590932\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 + 4x^4 + 6x^2 + 3$ |
| 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 |
|
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(3.359562\) |
\(0.839890\) |
$[40908,115154025,1158334769067,-263424]$ |
$[10227,-440104,18634308,-779615725,-2058]$ |
$[-108724120940360583/2,228746634549804,-947031470154]$ |
$y^2 + (x^3 + 1)y = 5x^6 - 4x^5 - 5x^4 + 14x^3 - 5x^2 - 4x + 5$ |
| 2058.a.16464.1 |
2058.a |
\( 2 \cdot 3 \cdot 7^{3} \) |
\( - 2^{4} \cdot 3 \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.270.2 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.719123\) |
\(0.839890\) |
$[16716,21945,119839251,2107392]$ |
$[4179,726754,168337344,43827596015,16464]$ |
$[1238643936365031/16,25772655805407/8,178562334636]$ |
$y^2 + (x^3 + 1)y = -3x^6 + 5x^5 - 11x^4 + 10x^3 - 11x^2 + 5x - 3$ |
| 2080.a.4160.1 |
2080.a |
\( 2^{5} \cdot 5 \cdot 13 \) |
\( - 2^{6} \cdot 5 \cdot 13 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.375514\) |
\(7.057076\) |
\(0.331254\) |
$[49728,2307,38240328,520]$ |
$[49728,103034878,284642525440,884629355151359,4160]$ |
$[4751437160558113062912/65,197973593207882440704/65,169203148053037056]$ |
$y^2 + xy = x^6 + 12x^4 + 48x^2 + 65$ |
| 2080.a.4160.2 |
2080.a |
\( 2^{5} \cdot 5 \cdot 13 \) |
\( 2^{6} \cdot 5 \cdot 13 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.375514\) |
\(7.057076\) |
\(0.331254\) |
$[49728,2307,38240328,520]$ |
$[49728,103034878,284642525440,884629355151359,4160]$ |
$[4751437160558113062912/65,197973593207882440704/65,169203148053037056]$ |
$y^2 + xy = x^6 - 12x^4 + 48x^2 - 65$ |
| 2176.a.69632.2 |
2176.a |
\( 2^{7} \cdot 17 \) |
\( - 2^{12} \cdot 17 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(4.167648\) |
\(0.694608\) |
$[7572,68115,166006308,272]$ |
$[15144,9374224,7623276544,6892706095040,69632]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + xy = x^6 + 9x^4 + 24x^2 + 17$ |
| 2176.a.69632.1 |
2176.a |
\( 2^{7} \cdot 17 \) |
\( 2^{12} \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(16.670591\) |
\(0.694608\) |
$[7572,68115,166006308,272]$ |
$[15144,9374224,7623276544,6892706095040,69632]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + xy = x^6 - 9x^4 + 24x^2 - 17$ |
| 2430.b.196830.1 |
2430.b |
\( 2 \cdot 3^{5} \cdot 5 \) |
\( - 2 \cdot 3^{9} \cdot 5 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.089147\) |
\(0.787683\) |
$[103200,92148840,2874875039973,-3240]$ |
$[154800,860236740,5905731060081,43549979813677800,-196830]$ |
$[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$ |
$y^2 + xy = 9x^5 - 30x^4 - 30x^3 + 92x^2 + 77x + 15$ |
| 2484.a.9936.1 |
2484.a |
\( 2^{2} \cdot 3^{3} \cdot 23 \) |
\( - 2^{4} \cdot 3^{3} \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(5.060189\) |
\(0.843365\) |
$[27960,133920,1232036820,39744]$ |
$[13980,8121030,6274451520,5441425997175,9936]$ |
$[1236095741507400000/23,51362822628555000/23,123418006728000]$ |
$y^2 + (x^3 + x)y = -x^6 - 8x^4 - 24x^2 - 23$ |
| 2592.b.419904.1 |
2592.b |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{8} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(8.188197\) |
\(0.682350\) |
$[96,180,5256,216]$ |
$[288,2376,15552,-291600,419904]$ |
$[4718592,135168,3072]$ |
$y^2 + x^3y = 2x^3 - 6x^2 + 6x - 2$ |
| 2624.a.2624.1 |
2624.a |
\( 2^{6} \cdot 41 \) |
\( - 2^{6} \cdot 41 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.898828\) |
\(6.802922\) |
\(0.382166\) |
$[8412,18219,50278164,328]$ |
$[8412,2936260,1361577856,707992534268,2624]$ |
$[658137058904811888/41,27309410584621020/41,36717844391136]$ |
$y^2 + (x^3 + x)y = 4x^4 + 24x^2 + 41$ |
| 2624.a.2624.2 |
2624.a |
\( 2^{6} \cdot 41 \) |
\( 2^{6} \cdot 41 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.224707\) |
\(6.802922\) |
\(0.382166\) |
$[8412,18219,50278164,328]$ |
$[8412,2936260,1361577856,707992534268,2624]$ |
$[658137058904811888/41,27309410584621020/41,36717844391136]$ |
$y^2 + (x^3 + x)y = -5x^4 + 24x^2 - 41$ |
| 3024.a.48384.1 |
3024.a |
\( 2^{4} \cdot 3^{3} \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(8.181413\) |
\(0.681784\) |
$[78,180,4338,189]$ |
$[156,534,-1260,-120429,48384]$ |
$[13366548/7,586599/14,-2535/4]$ |
$y^2 = x^5 + x^4 + 3x^3 + x^2 + x$ |
| 3024.b.145152.1 |
3024.b |
\( 2^{4} \cdot 3^{3} \cdot 7 \) |
\( - 2^{8} \cdot 3^{4} \cdot 7 \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{3} \) |
\(1.000000\) |
\(9.213670\) |
\(0.767806\) |
$[330,180,17190,567]$ |
$[660,17670,631260,26100675,145152]$ |
$[6039412500/7,489974375/14,7577625/4]$ |
$y^2 = x^6 - 2x^5 + 5x^4 - 5x^3 + 5x^2 - 2x + 1$ |
| 3072.a.3072.1 |
3072.a |
\( 2^{10} \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.499530\) |
\(0.656221\) |
$[48,24,636,12]$ |
$[96,320,-768,-44032,3072]$ |
$[2654208,92160,-2304]$ |
$y^2 = x^5 + x^4 + 2x^3 + x^2 + x$ |
| 3072.a.196608.1 |
3072.a |
\( 2^{10} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.249765\) |
\(0.656221\) |
$[2376,321,254043,24]$ |
$[9504,3760160,1981759488,1173959737088,196608]$ |
$[394394593494528,16418157695280,910463659776]$ |
$y^2 = -2x^6 - 9x^4 - 13x^2 - 6$ |
| 3072.a.196608.2 |
3072.a |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.499530\) |
\(0.656221\) |
$[2376,321,254043,24]$ |
$[9504,3760160,1981759488,1173959737088,196608]$ |
$[394394593494528,16418157695280,910463659776]$ |
$y^2 = 6x^6 - 13x^4 + 9x^2 - 2$ |
| 3072.b.3072.1 |
3072.b |
\( 2^{10} \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.286124\) |
\(0.767883\) |
$[48,24,636,12]$ |
$[96,320,-768,-44032,3072]$ |
$[2654208,92160,-2304]$ |
$y^2 = x^5 - x^4 + 2x^3 - x^2 + x$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.143062\) |
\(0.767883\) |
$[2376,321,254043,24]$ |
$[9504,3760160,1981759488,1173959737088,196608]$ |
$[394394593494528,16418157695280,910463659776]$ |
$y^2 = 2x^6 + 9x^4 + 13x^2 + 6$ |
| 3072.b.196608.1 |
3072.b |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.286124\) |
\(0.767883\) |
$[2376,321,254043,24]$ |
$[9504,3760160,1981759488,1173959737088,196608]$ |
$[394394593494528,16418157695280,910463659776]$ |
$y^2 = 2x^6 - 9x^4 + 13x^2 - 6$ |
| 3240.a.58320.1 |
3240.a |
\( 2^{3} \cdot 3^{4} \cdot 5 \) |
\( 2^{4} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(10.347832\) |
\(0.574880\) |
$[64,1440,11244,-960]$ |
$[96,-1776,25916,-166560,-58320]$ |
$[-2097152/15,1212416/45,-1658624/405]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 + 2x^2 - 3x$ |
| 3456.c.442368.1 |
3456.c |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(4.927633\) |
\(0.821272\) |
$[384,2295,331704,54]$ |
$[1536,73824,-36864,-1376651520,442368]$ |
$[19327352832,604766208,-196608]$ |
$y^2 + x^3y = x^4 - 3x^2 - 12$ |
| 3456.d.442368.1 |
3456.d |
\( 2^{7} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.4, 3.360.2 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.237423\) |
\(0.654678\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = -x^6 - 4x^4 - 6x^2 - 3$ |
| 3456.e.442368.1 |
3456.e |
\( 2^{7} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(16.844313\) |
\(0.701846\) |
$[384,2295,331704,54]$ |
$[1536,73824,-36864,-1376651520,442368]$ |
$[19327352832,604766208,-196608]$ |
$y^2 + x^3y = -x^4 - 3x^2 + 12$ |
| 3564.a.128304.1 |
3564.a |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( - 2^{4} \cdot 3^{6} \cdot 11 \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.075643\) |
\(18.922950\) |
\(0.477129\) |
$[904,15840,5450316,2112]$ |
$[1356,52854,-1629760,-1250874969,128304]$ |
$[1179158514752/33,101683837384/99,-1891855040/81]$ |
$y^2 + (x^3 + x)y = -2x^4 - x^2 + 11$ |
| 3584.b.229376.1 |
3584.b |
\( 2^{9} \cdot 7 \) |
\( - 2^{15} \cdot 7 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.90.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.059980\) |
\(17.689513\) |
\(0.530508\) |
$[420,3963,638988,28]$ |
$[1680,75328,-5648384,-3790898176,229376]$ |
$[58344300000,1557171000,-69501600]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -6x^4 + 34x^2 - 68x + 40$ |
| 3584.c.458752.1 |
3584.c |
\( 2^{9} \cdot 7 \) |
\( 2^{16} \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.2160.9 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.475514\) |
\(0.868879\) |
$[828,16635,5308452,56]$ |
$[3312,279616,-54648832,-64795509760,458752]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + x^3y = x^6 - 4x^5 - 13x^4 - 22x^3 - 21x^2 - 12x - 4$ |
| 3645.a.10935.1 |
3645.a |
\( 3^{6} \cdot 5 \) |
\( - 3^{7} \cdot 5 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.059091\) |
\(20.041234\) |
\(0.394755\) |
$[72,180,4032,180]$ |
$[108,216,-1080,-40824,10935]$ |
$[6718464/5,124416/5,-1152]$ |
$y^2 + x^3y = x^3 + 3x^2 + 3x + 1$ |
| 3645.a.295245.1 |
3645.a |
\( 3^{6} \cdot 5 \) |
\( 3^{10} \cdot 5 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.15.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.059091\) |
\(20.041234\) |
\(0.394755\) |
$[376,7380,710544,4860]$ |
$[564,2184,17960,1339896,295245]$ |
$[234849287168/1215,4837321216/3645,126955648/6561]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^5 - 7x^3 + x$ |
| 4096.a.65536.1 |
4096.a |
\( 2^{12} \) |
\( - 2^{16} \) |
$1$ |
$2$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$2$ |
2.90.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.432331\) |
\(21.167670\) |
\(0.571965\) |
$[72,894,30654,8]$ |
$[288,-6080,-925696,-75891712,65536]$ |
$[30233088,-2216160,-1171584]$ |
$y^2 + x^3y = -2x^4 + 3x^2 + 4$ |
| 4096.c.65536.1 |
4096.c |
\( 2^{12} \) |
\( 2^{16} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.2, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.203720\) |
\(0.900465\) |
$[72,894,30654,8]$ |
$[288,-6080,-925696,-75891712,65536]$ |
$[30233088,-2216160,-1171584]$ |
$y^2 + x^3y = 2x^4 + 3x^2 - 4$ |
| 4096.d.524288.1 |
4096.d |
\( 2^{12} \) |
\( - 2^{19} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.483901\) |
\(0.935488\) |
$[168,39,2121,2]$ |
$[1344,73600,5275648,418377728,524288]$ |
$[8364238848,340804800,18176256]$ |
$y^2 + x^3y = 2x^4 + 6x^2 + 8$ |
| 4096.f.524288.1 |
4096.f |
\( 2^{12} \) |
\( 2^{19} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(5.093799\) |
\(0.636725\) |
$[168,39,2121,2]$ |
$[1344,73600,5275648,418377728,524288]$ |
$[8364238848,340804800,18176256]$ |
$y^2 + x^3y = -2x^4 + 6x^2 - 8$ |
