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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
196.a.21952.1 |
196.a |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/6\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$6$ |
$0$ |
2.360.3, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(11.777148\) |
\(0.109048\) |
$[1340,1345,149855,2809856]$ |
$[335,4620,90160,2214800,21952]$ |
$[4219140959375/21952,6203236875/784,12905875/28]$ |
$y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$ |
249.a.6723.1 |
249.a |
\( 3 \cdot 83 \) |
\( - 3^{4} \cdot 83 \) |
$0$ |
$1$ |
$\Z/28\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[324526850403/83,25281736298/249,-4178776252/747]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
256.a.512.1 |
256.a |
\( 2^{8} \) |
\( - 2^{9} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$6$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
324.a.648.1 |
324.a |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(29.135501\) |
\(0.198201\) |
$[36,1569,-13743,99328]$ |
$[9,-62,356,-160,776]$ |
$[59049/776,-22599/388,7209/194]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$ |
394.a.3152.1 |
394.a |
\( 2 \cdot 197 \) |
\( 2^{4} \cdot 197 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[80,-20,649,-12608]$ |
$[40,70,39,-835,-3152]$ |
$[-6400000/197,-280000/197,-3900/197]$ |
$y^2 + (x + 1)y = -x^5$ |
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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[364,3529,393211,345600]$ |
$[91,198,0,-9801,2700]$ |
$[6240321451/2700,8289281/150,0]$ |
$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$ |
574.a.293888.1 |
574.a |
\( 2 \cdot 7 \cdot 41 \) |
\( - 2^{10} \cdot 7 \cdot 41 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(1.000000\) |
\(11.546350\) |
\(0.288659\) |
$[68,-55823,-955895,-37617664]$ |
$[17,2338,2304,-1356769,-293888]$ |
$[-1419857/293888,-820471/20992,-2601/1148]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$ |
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.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 |
✓ |
✓ |
$1$ |
\( 2^{5} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[18072,38904,233095932,1800000]$ |
$[9036,3395570,1698206400,953774351375,450000]$ |
$[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ |
$y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$ |
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 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(20.169780\) |
\(0.320155\) |
$[204,3273,161211,692224]$ |
$[51,-28,0,-196,5408]$ |
$[345025251/5408,-928557/1352,0]$ |
$y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$ |
688.a.2752.1 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{6} \cdot 43 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(25.707298\) |
\(0.321341\) |
$[32,112,-680,-344]$ |
$[32,-32,1344,10496,-2752]$ |
$[-524288/43,16384/43,-21504/43]$ |
$y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$ |
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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 + 1$ |
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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[436,3373,434667,4896]$ |
$[436,5672,77824,439920,39168]$ |
$[61544958196/153,1836351122/153,57789184/153]$ |
$y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$ |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.196056\) |
\(20.305961\) |
\(0.159244\) |
$[120,276,6864,3388]$ |
$[60,104,504,4856,847]$ |
$[777600000/847,22464000/847,259200/121]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$ |
966.a.834624.1 |
966.a |
\( 2 \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{6} \cdot 3^{4} \cdot 7 \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(1.000000\) |
\(9.526771\) |
\(0.396949\) |
$[92,24673,-557265,-106831872]$ |
$[23,-1006,14336,-170577,-834624]$ |
$[-279841/36288,266087/18144,-736/81]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1$ |
1083.a.1083.1 |
1083.a |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.075149\) |
\(22.662454\) |
\(0.189229\) |
$[56,244,928,4332]$ |
$[28,-8,264,1832,1083]$ |
$[17210368/1083,-175616/1083,68992/361]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3$ |
1145.a.143125.1 |
1145.a |
\( 5 \cdot 229 \) |
\( - 5^{4} \cdot 229 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.026504\) |
\(7.396287\) |
\(0.196028\) |
$[5004,191097,289856403,18320000]$ |
$[1251,57246,3273124,204393402,143125]$ |
$[3063984390631251/143125,112077149104746/143125,5122442333124/143125]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$ |
1192.a.19072.1 |
1192.a |
\( 2^{3} \cdot 149 \) |
\( - 2^{7} \cdot 149 \) |
$0$ |
$1$ |
$\Z/22\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 11 \) |
\(1.000000\) |
\(22.627068\) |
\(0.514252\) |
$[160,3184,271780,76288]$ |
$[80,-264,-17220,-361824,19072]$ |
$[25600000/149,-1056000/149,-861000/149]$ |
$y^2 + (x^3 + x)y = x^3 - 2x^2 - x + 1$ |
1253.b.1253.1 |
1253.b |
\( 7 \cdot 179 \) |
\( - 7 \cdot 179 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009941\) |
\(18.851977\) |
\(0.187411\) |
$[348,2409,250779,160384]$ |
$[87,215,467,-1399,1253]$ |
$[4984209207/1253,141578145/1253,3534723/1253]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^2$ |
1300.a.130000.1 |
1300.a |
\( 2^{2} \cdot 5^{2} \cdot 13 \) |
\( - 2^{4} \cdot 5^{4} \cdot 13 \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.90.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.093879\) |
\(7.601599\) |
\(0.237876\) |
$[4600,9904,15140164,520000]$ |
$[2300,218766,27536704,3868964111,130000]$ |
$[6436343000000/13,266172592200/13,1120532032]$ |
$y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13$ |
1312.a.2624.1 |
1312.a |
\( 2^{5} \cdot 41 \) |
\( - 2^{6} \cdot 41 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.028941\) |
\(16.518821\) |
\(0.239039\) |
$[112,91,1912,328]$ |
$[112,462,3440,42959,2624]$ |
$[275365888/41,10141824/41,674240/41]$ |
$y^2 + (x + 1)y = x^6 + 2x^5 + 3x^4 + 2x^3 + x^2$ |
1312.c.671744.1 |
1312.c |
\( 2^{5} \cdot 41 \) |
\( - 2^{14} \cdot 41 \) |
$0$ |
$1$ |
$\Z/22\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 11 \) |
\(1.000000\) |
\(11.857814\) |
\(0.538992\) |
$[164,1441,58489,83968]$ |
$[164,160,1984,74944,671744]$ |
$[2825761/16,8405/8,1271/16]$ |
$y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$ |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.179570\) |
\(30.476389\) |
\(0.218906\) |
$[88,2068,83248,5324]$ |
$[44,-264,-4840,-70664,1331]$ |
$[123904,-16896,-7040]$ |
$y^2 + x^3y = -x^4 - x^3 + 2x^2 + 3x + 1$ |
1338.a.2676.1 |
1338.a |
\( 2 \cdot 3 \cdot 223 \) |
\( - 2^{2} \cdot 3 \cdot 223 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.029284\) |
\(15.069119\) |
\(0.220645\) |
$[716,985,119011,342528]$ |
$[179,1294,13664,192855,2676]$ |
$[183765996899/2676,3710764333/1338,109452056/669]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 2x^2 + x + 1$ |
1369.a.1369.1 |
1369.a |
\( 37^{2} \) |
\( 37^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.30.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.102223\) |
\(19.550666\) |
\(0.222058\) |
$[24,-300,-2976,-5476]$ |
$[12,56,168,-280,-1369]$ |
$[-248832/1369,-96768/1369,-24192/1369]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^3 - x^2$ |
1490.a.1490.1 |
1490.a |
\( 2 \cdot 5 \cdot 149 \) |
\( - 2 \cdot 5 \cdot 149 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.038412\) |
\(24.373454\) |
\(0.234059\) |
$[1108,2617,932621,-190720]$ |
$[277,3088,44636,707107,-1490]$ |
$[-1630793025157/1490,-32816072552/745,-1712437822/745]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^3 - 2x^2 + 2x$ |
1519.a.1519.1 |
1519.a |
\( 7^{2} \cdot 31 \) |
\( - 7^{2} \cdot 31 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.40.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011133\) |
\(23.937241\) |
\(0.266486\) |
$[804,1953,517041,-194432]$ |
$[201,1602,16160,170439,-1519]$ |
$[-328080401001/1519,-13009202802/1519,-652880160/1519]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 2x^2 - x - 1$ |
1573.a.190333.1 |
1573.a |
\( 11^{2} \cdot 13 \) |
\( 11^{4} \cdot 13 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.480068\) |
\(2.500245\) |
\(0.240057\) |
$[38120,8596,107715056,761332]$ |
$[19060,15135384,16023823816,19083558276376,190333]$ |
$[2515443004991977600000/190333,9527291378032704000/17303,336426770019200/11]$ |
$y^2 + x^3y = -7x^4 - 7x^3 + 38x^2 + 21x - 83$ |
1647.a.1647.1 |
1647.a |
\( 3^{3} \cdot 61 \) |
\( 3^{3} \cdot 61 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.016225\) |
\(17.240672\) |
\(0.279723\) |
$[36,-639,16641,210816]$ |
$[9,30,-296,-891,1647]$ |
$[2187/61,810/61,-888/61]$ |
$y^2 + (x^3 + x + 1)y = x^5$ |
1655.a.206875.1 |
1655.a |
\( 5 \cdot 331 \) |
\( - 5^{4} \cdot 331 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.036902\) |
\(6.712019\) |
\(0.247686\) |
$[11444,-79223,-306097691,-26480000]$ |
$[2861,344356,55836816,10292018960,-206875]$ |
$[-191685511916770301/206875,-8064198843467636/206875,-457042262577936/206875]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 7x^3 + 2x^2 + 14x - 10$ |
1689.a.45603.1 |
1689.a |
\( 3 \cdot 563 \) |
\( - 3^{4} \cdot 563 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.055530\) |
\(9.013663\) |
\(0.250263\) |
$[34900,-37799,-434488675,-5837184]$ |
$[8725,3173476,1539708400,840751466856,-45603]$ |
$[-50562341569814453125/45603,-2107810313223812500/45603,-117211264267750000/45603]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 6x^4 + 21x^3 + 15x^2 + 3x$ |
1753.a.1753.1 |
1753.a |
\( 1753 \) |
\( -1753 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011436\) |
\(22.364636\) |
\(0.255772\) |
$[108,1497,18531,224384]$ |
$[27,-32,256,1472,1753]$ |
$[14348907/1753,-629856/1753,186624/1753]$ |
$y^2 + (x^3 + 1)y = x^2$ |
1776.b.191808.1 |
1776.b |
\( 2^{4} \cdot 3 \cdot 37 \) |
\( 2^{6} \cdot 3^{4} \cdot 37 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 5 \) |
\(1.000000\) |
\(11.389538\) |
\(0.569477\) |
$[32,-1136,-7560,23976]$ |
$[32,800,64,-159488,191808]$ |
$[524288/2997,409600/2997,1024/2997]$ |
$y^2 + y = 2x^5 + x^4 - x^2$ |
1777.a.1777.1 |
1777.a |
\( 1777 \) |
\( 1777 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039015\) |
\(7.694781\) |
\(0.300215\) |
$[6052,-1391,-2704039,227456]$ |
$[1513,95440,8030588,760371511,1777]$ |
$[7928565897078793/1777,330557651801680/1777,18383373101372/1777]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + 7x^2 - x - 8$ |
1861.a.1861.1 |
1861.a |
\( 1861 \) |
\( 1861 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017479\) |
\(17.654095\) |
\(0.308580\) |
$[60,3057,16311,-238208]$ |
$[15,-118,312,-2311,-1861]$ |
$[-759375/1861,398250/1861,-70200/1861]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2$ |
1863.a.1863.1 |
1863.a |
\( 3^{4} \cdot 23 \) |
\( - 3^{4} \cdot 23 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.40.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009664\) |
\(23.750143\) |
\(0.229523\) |
$[3588,6921,8059509,-238464]$ |
$[897,33237,1630597,89486835,-1863]$ |
$[-311709013239,-12876157827,-6338130539/9]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 + 4x^4 - 5x^2 + x$ |
1904.a.487424.1 |
1904.a |
\( 2^{4} \cdot 7 \cdot 17 \) |
\( - 2^{12} \cdot 7 \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 5 \) |
\(1.000000\) |
\(12.929331\) |
\(0.646467\) |
$[172,-1091,-23251,60928]$ |
$[172,1960,-2304,-1059472,487424]$ |
$[147008443/476,2782745/136,-16641/119]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^2 - x + 1$ |
1908.a.183168.1 |
1908.a |
\( 2^{2} \cdot 3^{2} \cdot 53 \) |
\( 2^{7} \cdot 3^{3} \cdot 53 \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(1.000000\) |
\(14.084505\) |
\(0.586854\) |
$[556,8089,1394947,-23445504]$ |
$[139,468,-144,-59760,-183168]$ |
$[-51888844699/183168,-34913047/5088,19321/1272]$ |
$y^2 + (x^3 + 1)y = 2x^4 + 3x^3 + 4x^2 + 2x$ |
1923.b.17307.1 |
1923.b |
\( 3 \cdot 641 \) |
\( - 3^{3} \cdot 641 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.009252\) |
\(11.343821\) |
\(0.314864\) |
$[1692,10929,5898807,2215296]$ |
$[423,7000,146780,3271985,17307]$ |
$[501577530309/641,19622547000/641,972711060/641]$ |
$y^2 + (x^3 + x + 1)y = x^4 + 3x^2 + x + 2$ |
1936.a.1936.1 |
1936.a |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.120.2, 3.360.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.350128\) |
\(19.381269\) |
\(0.271437\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = -x^6 + 2x^4 - x^2$ |
1973.a.1973.1 |
1973.a |
\( 1973 \) |
\( 1973 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011902\) |
\(23.025682\) |
\(0.274050\) |
$[80,148,7256,-7892]$ |
$[40,42,-384,-4281,-1973]$ |
$[-102400000/1973,-2688000/1973,614400/1973]$ |
$y^2 + y = x^6 - x^5 + x^2 - x$ |
1985.a.1985.1 |
1985.a |
\( 5 \cdot 397 \) |
\( - 5 \cdot 397 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.041851\) |
\(25.967882\) |
\(0.271696\) |
$[428,1705,359371,254080]$ |
$[107,406,-44,-42386,1985]$ |
$[14025517307/1985,497367458/1985,-503756/1985]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 - x$ |
1987.a.1987.1 |
1987.a |
\( 1987 \) |
\( 1987 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017829\) |
\(17.614068\) |
\(0.314034\) |
$[452,1129,100197,254336]$ |
$[113,485,3425,37950,1987]$ |
$[18424351793/1987,699805045/1987,43733825/1987]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2 - x - 1$ |
2001.a.2001.1 |
2001.a |
\( 3 \cdot 23 \cdot 29 \) |
\( 3 \cdot 23 \cdot 29 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.018980\) |
\(16.938296\) |
\(0.321482\) |
$[100,97,10385,256128]$ |
$[25,22,-80,-621,2001]$ |
$[9765625/2001,343750/2001,-50000/2001]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3$ |
2007.a.6021.1 |
2007.a |
\( 3^{2} \cdot 223 \) |
\( - 3^{3} \cdot 223 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037139\) |
\(15.293007\) |
\(0.283981\) |
$[588,6777,1216467,770688]$ |
$[147,618,1988,-22422,6021]$ |
$[2542277241/223,72707082/223,4773188/669]$ |
$y^2 + (x^2 + x + 1)y = x^6 + x^4$ |
2020.a.646400.1 |
2020.a |
\( 2^{2} \cdot 5 \cdot 101 \) |
\( - 2^{8} \cdot 5^{2} \cdot 101 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.023673\) |
\(7.797718\) |
\(0.276890\) |
$[394,1648,195485,2525]$ |
$[788,21478,704476,23455651,646400]$ |
$[1186837123028/2525,82103660647/5050,6835002271/10100]$ |
$y^2 + x^3y = 2x^4 - x^3 + 5x^2 - 4x + 4$ |