| 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 |
| 277.a.277.2 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.578417\) |
\(0.143137\) |
$[4480,1370512,1511819744,-1108]$ |
$[2240,-19352,164384,-1569936,-277]$ |
$[-56394933862400000/277,217505333248000/277,-824813158400/277]$ |
$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.196056\) |
\(20.305961\) |
\(0.159244\) |
$[120,276,6864,3388]$ |
$[60,104,504,4856,847]$ |
$[777600000/847,22464000/847,259200/121]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$ |
| 961.a.961.2 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.616097\) |
\(0.449288\) |
$[11260,503521,1770579599,123008]$ |
$[2815,309196,43449708,6677190401,961]$ |
$[176763257309509375/961,6897140364776500/961,344305262376300/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$ |
| 961.a.961.3 |
961.a |
\( 31^{2} \) |
\( 31^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.232193\) |
\(0.449288\) |
$[260,1681,185209,123008]$ |
$[65,106,-672,-13729,961]$ |
$[1160290625/961,29110250/961,-2839200/961]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$ |
| 961.a.923521.1 |
961.a |
\( 31^{2} \) |
\( 31^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(2.246439\) |
\(0.449288\) |
$[4100,78961,94151689,118210688]$ |
$[1025,40486,2121888,133954751,923521]$ |
$[1131408212890625/923521,1406419156250/29791,2319780000/961]$ |
$y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$ |
| 968.a.1936.1 |
968.a |
\( 2^{3} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.080529\) |
\(26.986750\) |
\(0.173857\) |
$[120,357,14937,242]$ |
$[120,362,-1344,-73081,1936]$ |
$[1555200000/121,39096000/121,-1209600/121]$ |
$y^2 + y = x^6 - x^4$ |
| 968.a.234256.1 |
968.a |
\( 2^{3} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{4} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.080529\) |
\(5.397350\) |
\(0.173857\) |
$[23544,6117,47655081,29282]$ |
$[23544,23092586,30194746560,44409396210311,234256]$ |
$[452148675314325387264/14641,1712381980706754624/1331,785948064456960/11]$ |
$y^2 + x^3y = 6x^4 + 47x^2 + 121$ |
| 1077.b.1077.1 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.157286\) |
\(0.406291\) |
$[320,544,55360,4308]$ |
$[160,976,7360,56256,1077]$ |
$[104857600000/1077,3997696000/1077,188416000/1077]$ |
$y^2 + x^3y = x^5 + x^4 - x - 2$ |
| 1109.c.1109.1 |
1109.c |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.552149\) |
\(0.382086\) |
$[392,292,36703,4436]$ |
$[196,1552,16001,181873,1109]$ |
$[289254654976/1109,11685839872/1109,614694416/1109]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - 2x^2 - 1$ |
| 1164.a.1164.1 |
1164.a |
\( 2^{2} \cdot 3 \cdot 97 \) |
\( 2^{2} \cdot 3 \cdot 97 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.402119\) |
\(0.456085\) |
$[500,-47,46665,148992]$ |
$[125,653,3805,12304,1164]$ |
$[30517578125/1164,1275390625/1164,59453125/1164]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 - 1$ |
| 1210.a.1210.1 |
1210.a |
\( 2 \cdot 5 \cdot 11^{2} \) |
\( 2 \cdot 5 \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.20.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.627716\) |
\(0.345109\) |
$[208,75964,-1718663,-4840]$ |
$[104,-12210,559319,-22728731,-1210]$ |
$[-6083264512/605,124859904/11,-3024797152/605]$ |
$y^2 + (x^3 + x)y = 3x^3 - 2x^2 + 6x + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.179570\) |
\(30.476389\) |
\(0.218906\) |
$[88,2068,83248,5324]$ |
$[44,-264,-4840,-70664,1331]$ |
$[123904,-16896,-7040]$ |
$y^2 + x^3y = -x^4 - x^3 + 2x^2 + 3x + 1$ |
| 1532.a.1532.1 |
1532.a |
\( 2^{2} \cdot 383 \) |
\( 2^{2} \cdot 383 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.961311\) |
\(0.518452\) |
$[372,2673,322425,196096]$ |
$[93,249,261,-9432,1532]$ |
$[6956883693/1532,200284893/1532,2257389/1532]$ |
$y^2 + (x^3 + 1)y = -x - 1$ |
| 1573.a.1573.1 |
1573.a |
\( 11^{2} \cdot 13 \) |
\( 11^{2} \cdot 13 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.480068\) |
\(12.501224\) |
\(0.240057\) |
$[200,916,59936,6292]$ |
$[100,264,-104,-20024,1573]$ |
$[10000000000/1573,24000000/143,-80000/121]$ |
$y^2 + x^3y = -x^4 - 3x^3 - 4x^2 - 3x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.480068\) |
\(2.500245\) |
\(0.240057\) |
$[38120,8596,107715056,761332]$ |
$[19060,15135384,16023823816,19083558276376,190333]$ |
$[2515443004991977600000/190333,9527291378032704000/17303,336426770019200/11]$ |
$y^2 + x^3y = -7x^4 - 7x^3 + 38x^2 + 21x - 83$ |
| 1589.a.1589.1 |
1589.a |
\( 7 \cdot 227 \) |
\( 7 \cdot 227 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.424681\) |
\(0.536987\) |
$[480,1872,427680,6356]$ |
$[240,2088,5280,-773136,1589]$ |
$[796262400000/1589,28864512000/1589,304128000/1589]$ |
$y^2 + y = x^5 + 4x^4 + 4x^3 - x^2 - x$ |
| 1665.a.1665.1 |
1665.a |
\( 3^{2} \cdot 5 \cdot 37 \) |
\( - 3^{2} \cdot 5 \cdot 37 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(16.175945\) |
\(0.647038\) |
$[572,1969,296919,213120]$ |
$[143,770,5904,62843,1665]$ |
$[59797108943/1665,450327878/333,13414544/185]$ |
$y^2 + (x^3 + x^2 + 1)y = x^4 + x^3 + 2x^2 + 2x + 1$ |
| 1791.a.5373.1 |
1791.a |
\( 3^{2} \cdot 199 \) |
\( 3^{3} \cdot 199 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.123952\) |
\(26.794751\) |
\(0.265700\) |
$[480,5904,740016,21492]$ |
$[240,1416,15376,421296,5373]$ |
$[29491200000/199,724992000/199,98406400/597]$ |
$y^2 + y = 3x^5 + 6x^4 + 2x^3 - x^2$ |
| 1835.b.1835.1 |
1835.b |
\( 5 \cdot 367 \) |
\( - 5 \cdot 367 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.464262\) |
\(0.538570\) |
$[992,496,395968,-7340]$ |
$[496,10168,249856,5135088,-1835]$ |
$[-30019840638976/1835,-1240739381248/1835,-61468573696/1835]$ |
$y^2 + x^3y = -2x^4 + 4x^2 - x - 2$ |
| 1844.b.29504.1 |
1844.b |
\( 2^{2} \cdot 461 \) |
\( 2^{6} \cdot 461 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.216304\) |
\(0.568652\) |
$[276,-73935,-6159303,3776512]$ |
$[69,3279,27261,-2217708,29504]$ |
$[1564031349/29504,1077181011/29504,129789621/29504]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 2x^4 - 5x^3 + x$ |
| 1923.a.1923.1 |
1923.a |
\( 3 \cdot 641 \) |
\( - 3 \cdot 641 \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
|
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(8.754490\) |
\(0.700359\) |
$[1180,5521,2133607,246144]$ |
$[295,3396,48644,704291,1923]$ |
$[2234138434375/1923,29061128500/641,4233244100/1923]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + x^5 - 3x^4 + 2x^3 - 3x^2 + x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.350128\) |
\(19.381269\) |
\(0.271437\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = -x^6 + 2x^4 - x^2$ |
| 1936.b.1936.1 |
1936.b |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.120.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.505396\) |
\(0.420216\) |
$[120,357,14937,242]$ |
$[120,362,-1344,-73081,1936]$ |
$[1555200000/121,39096000/121,-1209600/121]$ |
$y^2 + y = -x^6 - x^4$ |
| 1936.b.234256.1 |
1936.b |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.120.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(2.101079\) |
\(0.420216\) |
$[23544,6117,47655081,29282]$ |
$[23544,23092586,30194746560,44409396210311,234256]$ |
$[452148675314325387264/14641,1712381980706754624/1331,785948064456960/11]$ |
$y^2 + x^3y = -6x^4 + 47x^2 - 121$ |
| 1989.a.1989.1 |
1989.a |
\( 3^{2} \cdot 13 \cdot 17 \) |
\( 3^{2} \cdot 13 \cdot 17 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.051733\) |
\(0.602069\) |
$[128,640,23104,7956]$ |
$[64,64,-64,-2048,1989]$ |
$[1073741824/1989,16777216/1989,-262144/1989]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x - 1$ |
| 1996.a.31936.1 |
1996.a |
\( 2^{2} \cdot 499 \) |
\( 2^{6} \cdot 499 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.676396\) |
\(0.547056\) |
$[1580,146065,58442167,-4087808]$ |
$[395,415,-1261,-167580,-31936]$ |
$[-9615801246875/31936,-25576398125/31936,196747525/31936]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + 4x + 3$ |
| 2001.b.2001.1 |
2001.b |
\( 3 \cdot 23 \cdot 29 \) |
\( 3 \cdot 23 \cdot 29 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.630616\) |
\(0.705225\) |
$[932,-1151,-435391,256128]$ |
$[233,2310,32224,543023,2001]$ |
$[686719856393/2001,9739989490/667,1749408736/2001]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^3 + x - 1$ |
| 2166.a.6498.1 |
2166.a |
\( 2 \cdot 3 \cdot 19^{2} \) |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.20.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.006193\) |
\(0.480495\) |
$[80,407884,-75901591,-25992]$ |
$[40,-67914,9188999,-1061187859,-6498]$ |
$[-51200000/3249,241472000/361,-7351199200/3249]$ |
$y^2 + (x^3 + x)y = x^5 + 3x^4 + 3x^3 - 15x - 9$ |
| 2261.a.2261.1 |
2261.a |
\( 7 \cdot 17 \cdot 19 \) |
\( 7 \cdot 17 \cdot 19 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.541499\) |
\(0.541660\) |
$[160,-80,2816,9044]$ |
$[80,280,576,-8080,2261]$ |
$[3276800000/2261,20480000/323,3686400/2261]$ |
$y^2 + y = x^5 + x^2 + x$ |
| 2348.a.2348.1 |
2348.a |
\( 2^{2} \cdot 587 \) |
\( 2^{2} \cdot 587 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.589807\) |
\(0.623592\) |
$[180,-1791,-63855,300544]$ |
$[45,159,165,-4464,2348]$ |
$[184528125/2348,14488875/2348,334125/2348]$ |
$y^2 + (x^2 + x + 1)y = -x^5 - x^2 - x$ |
| 2445.a.22005.1 |
2445.a |
\( 3 \cdot 5 \cdot 163 \) |
\( 3^{3} \cdot 5 \cdot 163 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.093556\) |
\(0.563742\) |
$[544,19984,2690720,-88020]$ |
$[272,-248,-736,-65424,-22005]$ |
$[-1488827973632/22005,4990664704/22005,54452224/22005]$ |
$y^2 + y = x^5 + 4x^4 - 4x^3 + 3x^2 - x$ |
| 2500.a.400000.1 |
2500.a |
\( 2^{2} \cdot 5^{4} \) |
\( - 2^{7} \cdot 5^{5} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.60.2, 3.2880.2 |
|
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.411821\) |
\(0.682364\) |
$[860,36865,8199455,16384]$ |
$[1075,9750,107500,5125000,400000]$ |
$[459401384375/128,1937983125/64,9938375/32]$ |
$y^2 + (x^3 + 1)y = -2x^6 - 2x^5 + 2x^3 - 2x - 2$ |
| 2540.a.2540.1 |
2540.a |
\( 2^{2} \cdot 5 \cdot 127 \) |
\( 2^{2} \cdot 5 \cdot 127 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.434542\) |
\(0.697382\) |
$[236,6769,348391,-325120]$ |
$[59,-137,259,-872,-2540]$ |
$[-714924299/2540,28136923/2540,-901579/2540]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 2x^4 + x^3 + x^2$ |
| 2613.a.2613.1 |
2613.a |
\( 3 \cdot 13 \cdot 67 \) |
\( 3 \cdot 13 \cdot 67 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(16.703789\) |
\(0.668152\) |
$[64,-944,-12048,10452]$ |
$[32,200,16,-9872,2613]$ |
$[33554432/2613,6553600/2613,16384/2613]$ |
$y^2 + y = x^5 + x^4 - x^2$ |
| 2677.a.2677.1 |
2677.a |
\( 2677 \) |
\( 2677 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.925763\) |
\(0.717031\) |
$[224,3088,171360,-10708]$ |
$[112,8,224,6256,-2677]$ |
$[-17623416832/2677,-11239424/2677,-2809856/2677]$ |
$y^2 + y = x^5 + 4x^4 + 4x^3 + 3x^2 + x$ |
| 2722.a.2722.1 |
2722.a |
\( 2 \cdot 1361 \) |
\( 2 \cdot 1361 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.720019\) |
\(0.468801\) |
$[248,868,71599,10888]$ |
$[124,496,1441,-16833,2722]$ |
$[14658125312/1361,472842752/1361,11078408/1361]$ |
$y^2 + (x^3 + x)y = -x^4 - x - 1$ |
| 3061.a.3061.1 |
3061.a |
\( 3061 \) |
\( 3061 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.851961\) |
\(0.554078\) |
$[160,508,26295,12244]$ |
$[80,182,145,-5381,3061]$ |
$[3276800000/3061,93184000/3061,928000/3061]$ |
$y^2 + (x + 1)y = -x^6 - x^5$ |
| 3088.a.12352.1 |
3088.a |
\( 2^{4} \cdot 193 \) |
\( - 2^{6} \cdot 193 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.124484\) |
\(18.252318\) |
\(0.454423\) |
$[108,393,12771,1544]$ |
$[108,224,-576,-28096,12352]$ |
$[229582512/193,4408992/193,-104976/193]$ |
$y^2 + x^3y = x^3 + 2x^2 + 2x + 1$ |
| 3098.a.3098.1 |
3098.a |
\( 2 \cdot 1549 \) |
\( 2 \cdot 1549 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.833118\) |
\(0.633325\) |
$[80,-20,631,12392]$ |
$[40,70,41,-815,3098]$ |
$[51200000/1549,2240000/1549,32800/1549]$ |
$y^2 + (x + 1)y = x^5$ |
| 3109.a.3109.1 |
3109.a |
\( 3109 \) |
\( 3109 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.601392\) |
\(17.682100\) |
\(0.425355\) |
$[8,-596,-1001,12436]$ |
$[4,100,1,-2499,3109]$ |
$[1024/3109,6400/3109,16/3109]$ |
$y^2 + (x^3 + x)y = -x^4 - x$ |
| 3125.a.3125.1 |
3125.a |
\( 5^{5} \) |
\( 5^{5} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{CM}\) |
\(\Q\) |
|
$F_{ac}$ |
|
✓ |
✓ |
$C_2$ |
$C_{10}$ |
$3$ |
$1$ |
2.36.1, 3.1296.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.957841\) |
\(0.718314\) |
$[0,0,0,4]$ |
$[0,0,0,0,3125]$ |
$[0,0,0]$ |
$y^2 + y = x^5$ |
| 3189.a.3189.1 |
3189.a |
\( 3 \cdot 1063 \) |
\( 3 \cdot 1063 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.466904\) |
\(22.021518\) |
\(0.411278\) |
$[160,532,27545,-12756]$ |
$[80,178,95,-6021,-3189]$ |
$[-3276800000/3189,-91136000/3189,-608000/3189]$ |
$y^2 + (x + 1)y = x^6 + x^5$ |
| 3211.b.3211.1 |
3211.b |
\( 13^{2} \cdot 19 \) |
\( - 13^{2} \cdot 19 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.813357\) |
\(0.752534\) |
$[384,-1872,-260208,-12844]$ |
$[192,1848,28656,521712,-3211]$ |
$[-260919263232/3211,-13079937024/3211,-1056374784/3211]$ |
$y^2 + x^3y = x^5 - 4x^3 - 3x^2 + 3x + 2$ |
| 3313.a.3313.1 |
3313.a |
\( 3313 \) |
\( -3313 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.834264\) |
\(0.993371\) |
$[732,13377,3198495,424064]$ |
$[183,838,-1904,-262669,3313]$ |
$[205236901143/3313,5135672106/3313,-63763056/3313]$ |
$y^2 + (x^3 + x^2 + 1)y = -x^2 - x + 1$ |
| 3364.a.215296.1 |
3364.a |
\( 2^{2} \cdot 29^{2} \) |
\( - 2^{8} \cdot 29^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.084841\) |
\(14.117726\) |
\(0.479103\) |
$[396,14217,1334619,27557888]$ |
$[99,-184,0,-8464,215296]$ |
$[9509900499/215296,-22316877/26912,0]$ |
$y^2 + (x^3 + 1)y = x^5 + 4x^4 + 5x^3 + 4x^2 + x$ |
| 3388.a.13552.1 |
3388.a |
\( 2^{2} \cdot 7 \cdot 11^{2} \) |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.145782\) |
\(20.156384\) |
\(0.352613\) |
$[1480,1189,561823,1694]$ |
$[1480,90474,7330624,665944711,13552]$ |
$[443801324800000/847,18331118088000/847,143366060800/121]$ |
$y^2 + y = x^6 - 4x^4 + 5x^2 - 2$ |
| 3436.a.3436.1 |
3436.a |
\( 2^{2} \cdot 859 \) |
\( 2^{2} \cdot 859 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.344465\) |
\(0.773779\) |
$[172,2593,110559,-439808]$ |
$[43,-31,-61,-896,-3436]$ |
$[-147008443/3436,2464717/3436,112789/3436]$ |
$y^2 + (x^2 + x + 1)y = -x^5$ |
| 3483.a.282123.1 |
3483.a |
\( 3^{4} \cdot 43 \) |
\( - 3^{8} \cdot 43 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.171629\) |
\(11.287117\) |
\(0.387439\) |
$[0,-432,2592,4644]$ |
$[0,648,7776,-104976,-282123]$ |
$[0,2654208/1849,-768/43]$ |
$y^2 + y = x^5 - x^4 - 2x^3 + x^2 - x$ |
| 3566.b.3566.1 |
3566.b |
\( 2 \cdot 1783 \) |
\( - 2 \cdot 1783 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.425594\) |
\(0.617024\) |
$[688,-3116,-672081,-14264]$ |
$[344,5450,119281,2832541,-3566]$ |
$[-2408586330112/1783,-110928166400/1783,-7057618208/1783]$ |
$y^2 + xy = x^5 - x^4 + 4x^3 - 8x^2 + 5x - 1$ |
| 3601.a.3601.1 |
3601.a |
\( 13 \cdot 277 \) |
\( - 13 \cdot 277 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.546649\) |
\(0.901866\) |
$[412,34369,3283039,460928]$ |
$[103,-990,-2096,-298997,3601]$ |
$[11592740743/3601,-1081799730/3601,-22236464/3601]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + x^2 - x + 1$ |
