| 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 |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.356066\) |
\(0.178033\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-\frac{1352659309173012149}{168},\frac{419870026410625699}{168},-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$ |
| 400.a.409600.1 |
400.a |
\( 2^{4} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.17280.4 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(7.977095\) |
\(0.221586\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[\frac{58632501248}{25},\frac{2327987904}{25},4674304]$ |
$y^2 = x^6 + 4x^4 + 4x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(1.000000\) |
\(11.546350\) |
\(0.288659\) |
$[68,-55823,-955895,-37617664]$ |
$[17,2338,2304,-1356769,-293888]$ |
$[-\frac{1419857}{293888},-\frac{820471}{20992},-\frac{2601}{1148}]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$ |
| 576.b.147456.1 |
576.b |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.7, 3.2160.25 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[\frac{5071050752}{9},\frac{195344320}{9},1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{5} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[18072,38904,233095932,1800000]$ |
$[9036,3395570,1698206400,953774351375,450000]$ |
$[\frac{418329622965299904}{3125},\frac{3479436045234936}{625},\frac{38515932506304}{125}]$ |
$y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.872985\) |
\(0.218246\) |
$[161796,1070662305,46065265919409,84410368]$ |
$[40449,23560804,14638854160,9253881697856,659456]$ |
$[\frac{108277681088425330677249}{659456},\frac{389810454818831018649}{164864},\frac{9297727292338785}{256}]$ |
$y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$ |
| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(1.113349\) |
\(0.278337\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-\frac{1352659309173012149}{168},\frac{419870026410625699}{168},-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(1.000000\) |
\(6.723260\) |
\(0.320155\) |
$[1620,52953,29527389,71991296]$ |
$[405,4628,-8112,-6175936,562432]$ |
$[\frac{10896201253125}{562432},\frac{5912281125}{10816},-\frac{492075}{208}]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$ |
| 688.a.704512.2 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{14} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(6.426825\) |
\(0.321341\) |
$[464,-248,-39602,-86]$ |
$[1856,146176,15688704,1937702912,-704512]$ |
$[-\frac{1344218660864}{43},-\frac{57041383424}{43},-\frac{3298550016}{43}]$ |
$y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$ |
| 688.a.704512.1 |
688.a |
\( 2^{4} \cdot 43 \) |
\( 2^{14} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(6.426825\) |
\(0.321341\) |
$[128,532,26830,86]$ |
$[512,5248,-408576,-59183104,704512]$ |
$[\frac{2147483648}{43},\frac{42991616}{43},-\frac{6537216}{43}]$ |
$y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$ |
| 708.a.181248.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{10} \cdot 3 \cdot 59 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.325344\) |
\(0.325344\) |
$[234100,3468879025,202585466081177,-23199744]$ |
$[58525,-1820975,60952909,62829762150,-181248]$ |
$[-\frac{686605237334059580078125}{181248},\frac{365029741228054296875}{181248},-\frac{208774418179643125}{181248}]$ |
$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(14.457058\) |
\(0.301189\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[\frac{54412363190235229024}{3645},\frac{251762275020280012}{405},\frac{310461362928064}{9}]$ |
$y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.731485\) |
\(0.358218\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[\frac{1248318403996}{2401},\frac{9291226221}{4802},-\frac{23245787}{9604}]$ |
$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(0.328982\) |
\(0.328982\) |
$[103200,92148840,2874875039973,-3240]$ |
$[154800,860236740,5905731060081,43549979813677800,-196830]$ |
$[-451609936896000000000,-16212110811776000000,-\frac{2156977131869584000}{3}]$ |
$y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$ |
| 830.a.830000.1 |
830.a |
\( 2 \cdot 5 \cdot 83 \) |
\( - 2^{4} \cdot 5^{4} \cdot 83 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.868729\) |
\(0.366796\) |
$[15236,-229487,-1147645831,-106240000]$ |
$[3809,614082,133745600,33085071919,-830000]$ |
$[-\frac{801779343712318049}{830000},-\frac{16967946642572289}{415000},-\frac{4851113741084}{2075}]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 16x^3 + 8x^2 + x$ |
| 847.d.456533.1 |
847.d |
\( 7 \cdot 11^{2} \) |
\( 7^{3} \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.2160.20 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(9.829455\) |
\(0.262119\) |
$[90952,10132,303847072,1826132]$ |
$[45476,86167752,217689875480,618695823148744,456533]$ |
$[\frac{194496275421254111077376}{456533},\frac{736713878289412204032}{41503},\frac{10847340081772160}{11}]$ |
$y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(9.071483\) |
\(0.377978\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 - 4x^4 + 6x^2 - 3$ |
| 880.a.225280.1 |
880.a |
\( 2^{4} \cdot 5 \cdot 11 \) |
\( - 2^{12} \cdot 5 \cdot 11 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.640.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.515082\) |
\(0.378770\) |
$[2342,111952,73574536,-880]$ |
$[4684,615622,103120196,26006137795,-225280]$ |
$[-\frac{2201833501574851}{220},-\frac{494259267301121}{1760},-\frac{35350660170809}{3520}]$ |
$y^2 = x^5 + 13x^4 + 55x^3 + 76x^2 - 44$ |
| 882.a.302526.1 |
882.a |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( - 2 \cdot 3^{2} \cdot 7^{5} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.542623\) |
\(0.391957\) |
$[2572,-283391,165464399,38723328]$ |
$[643,29035,-3791761,-820283387,302526]$ |
$[\frac{109914468611443}{302526},\frac{7718888172745}{302526},-\frac{1567699793689}{302526}]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5$ |
| 960.a.245760.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[120,213,10095,30]$ |
$[480,7328,-15360,-15268096,245760]$ |
$[103680000,3297600,-14400]$ |
$y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$ |
| 960.a.368640.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{13} \cdot 3^{2} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[8952,6072,17987052,1440]$ |
$[17904,13340192,13237770240,14762078945024,368640]$ |
$[\frac{24952719973569408}{5},\frac{1038436236963696}{5},11510985848256]$ |
$y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$ |
| 960.a.983040.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[9,33,666,120]$ |
$[36,-298,-34260,-330541,983040]$ |
$[\frac{19683}{320},-\frac{36207}{2560},-\frac{46251}{1024}]$ |
$y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(2.246439\) |
\(0.449288\) |
$[4100,78961,94151689,118210688]$ |
$[1025,40486,2121888,133954751,923521]$ |
$[\frac{1131408212890625}{923521},\frac{1406419156250}{29791},\frac{2319780000}{961}]$ |
$y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(1.000000\) |
\(9.526771\) |
\(0.396949\) |
$[92,24673,-557265,-106831872]$ |
$[23,-1006,14336,-170577,-834624]$ |
$[-\frac{279841}{36288},\frac{266087}{18144},-\frac{736}{81}]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.080529\) |
\(5.397350\) |
\(0.173857\) |
$[23544,6117,47655081,29282]$ |
$[23544,23092586,30194746560,44409396210311,234256]$ |
$[\frac{452148675314325387264}{14641},\frac{1712381980706754624}{1331},\frac{785948064456960}{11}]$ |
$y^2 + x^3y = 6x^4 + 47x^2 + 121$ |
| 976.a.999424.1 |
976.a |
\( 2^{4} \cdot 61 \) |
\( 2^{14} \cdot 61 \) |
$0$ |
$0$ |
$\Z/29\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,29$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 29 \) |
\(1.000000\) |
\(12.900365\) |
\(0.444840\) |
$[152,1012,68714,-124928]$ |
$[152,288,-24464,-950368,-999424]$ |
$[-\frac{4952198}{61},-\frac{61731}{61},\frac{551969}{976}]$ |
$y^2 + (x + 1)y = x^6 - 2x^5 + 2x^3 - x^2$ |
| 980.a.878080.1 |
980.a |
\( 2^{2} \cdot 5 \cdot 7^{2} \) |
\( - 2^{9} \cdot 5 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.2160.20 |
|
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(4.677173\) |
\(0.389764\) |
$[2508,50745,41700723,112394240]$ |
$[627,14266,359660,5497016,878080]$ |
$[\frac{96903107471907}{878080},\frac{251175228777}{62720},\frac{144278343}{896}]$ |
$y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$ |
| 990.a.240570.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{7} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(3.087468\) |
\(0.385934\) |
$[153028,6848257,343366646113,30792960]$ |
$[38257,60697908,127876480380,301983618580299,240570]$ |
$[\frac{81951056110393451083057}{240570},\frac{188813894774599018858}{13365},\frac{7001861848004294}{9}]$ |
$y^2 + (x^2 + x)y = 3x^5 + 28x^4 + 72x^3 + 28x^2 + 3x$ |
| 1050.a.131250.1 |
1050.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 3 \cdot 5^{5} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.612551\) |
\(0.413284\) |
$[11868,198609,759217863,16800000]$ |
$[2967,358520,56735700,9949557875,131250]$ |
$[\frac{76641937806559869}{43750},\frac{312136655012892}{4375},\frac{475666111026}{125}]$ |
$y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$ |
| 1083.b.390963.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{4} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.132919\) |
\(0.265837\) |
$[150440,1945515892,68956865081488,-1563852]$ |
$[75220,-88500632,98386538568,-107931608328616,-390963]$ |
$[-\frac{2408056349828975363200000}{390963},\frac{1982406707133537344000}{20577},-\frac{27053302090985600}{19}]$ |
$y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$ |
| 1104.b.141312.1 |
1104.b |
\( 2^{4} \cdot 3 \cdot 23 \) |
\( - 2^{11} \cdot 3 \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.712625\) |
\(0.356313\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[\frac{189267815942240625}{46},\frac{2008843709918625}{46},-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$ |
| 1116.a.214272.1 |
1116.a |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( - 2^{8} \cdot 3^{3} \cdot 31 \) |
$0$ |
$0$ |
$\Z/39\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \cdot 13 \) |
\(1.000000\) |
\(16.984099\) |
\(0.435490\) |
$[52,22201,238285,-27426816]$ |
$[13,-918,36,-210564,-214272]$ |
$[-\frac{371293}{214272},\frac{37349}{3968},-\frac{169}{5952}]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$ |
| 1125.a.151875.1 |
1125.a |
\( 3^{2} \cdot 5^{3} \) |
\( - 3^{5} \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(1.964402\) |
\(0.491100\) |
$[8600,612100,1556297975,-607500]$ |
$[4300,668400,132975225,31258726875,-151875]$ |
$[-\frac{2352135088000000}{243},-\frac{28342655360000}{81},-\frac{437104339600}{27}]$ |
$y^2 + xy = 15x^5 + 50x^4 + 55x^3 + 22x^2 + 3x$ |
| 1136.a.290816.1 |
1136.a |
\( 2^{4} \cdot 71 \) |
\( 2^{12} \cdot 71 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(13.476708\) |
\(0.481311\) |
$[9252,17217,52921881,36352]$ |
$[9252,3555168,1815712832,1039938903360,290816]$ |
$[\frac{66203075280122793}{284},\frac{1374792164318403}{142},\frac{151781365064097}{284}]$ |
$y^2 + (x^3 + x^2)y = -5x^4 - 9x^3 + 25x^2 + 40x - 24$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.026504\) |
\(7.396287\) |
\(0.196028\) |
$[5004,191097,289856403,18320000]$ |
$[1251,57246,3273124,204393402,143125]$ |
$[\frac{3063984390631251}{143125},\frac{112077149104746}{143125},\frac{5122442333124}{143125}]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$ |
| 1152.a.147456.1 |
1152.a |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.270694\) |
\(0.454418\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[\frac{5071050752}{9},\frac{195344320}{9},1016576]$ |
$y^2 = x^6 - 2x^4 + 2x^2 - 1$ |
| 1164.b.670464.1 |
1164.b |
\( 2^{2} \cdot 3 \cdot 97 \) |
\( 2^{8} \cdot 3^{3} \cdot 97 \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(1.000000\) |
\(8.941486\) |
\(0.425785\) |
$[372,4521,1271253,85819392]$ |
$[93,172,-10928,-261472,670464]$ |
$[\frac{257662359}{24832},\frac{1281013}{6208},-\frac{656363}{4656}]$ |
$y^2 + (x^2 + x + 1)y = 2x^5 - 2x^4 + x^3 - x^2$ |
| 1184.a.606208.2 |
1184.a |
\( 2^{5} \cdot 37 \) |
\( - 2^{14} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.116022\) |
\(0.444751\) |
$[352,316,34242,74]$ |
$[1408,79232,5831680,483323904,606208]$ |
$[\frac{337748426752}{37},\frac{13498597376}{37},\frac{705633280}{37}]$ |
$y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$ |
| 1184.a.606208.1 |
1184.a |
\( 2^{5} \cdot 37 \) |
\( 2^{14} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(14.232044\) |
\(0.444751\) |
$[176,496,29918,74]$ |
$[704,15360,140288,-34291712,606208]$ |
$[\frac{10554638336}{37},\frac{327106560}{37},\frac{4243712}{37}]$ |
$y^2 = 2x^5 + x^4 - 8x^3 - 8x^2 - 2x$ |
| 1197.a.410571.1 |
1197.a |
\( 3^{2} \cdot 7 \cdot 19 \) |
\( - 3^{2} \cdot 7^{4} \cdot 19 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.778043\) |
\(0.375561\) |
$[3296,706780,578353015,-1642284]$ |
$[1648,-4634,23921,4486963,-410571]$ |
$[-\frac{12155869717331968}{410571},\frac{2962986082304}{58653},-\frac{3419323136}{21609}]$ |
$y^2 + (x^2 + 1)y = x^5 + 12x^4 - 7x^3 - 3x^2 + x$ |
| 1200.a.450000.1 |
1200.a |
\( 2^{4} \cdot 3 \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{5} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.655371\) |
\(0.353461\) |
$[18072,38904,233095932,1800000]$ |
$[9036,3395570,1698206400,953774351375,450000]$ |
$[\frac{418329622965299904}{3125},\frac{3479436045234936}{625},\frac{38515932506304}{125}]$ |
$y^2 + (x^3 + x)y = 4x^4 + 25x^2 + 45$ |
| 1269.b.102789.1 |
1269.b |
\( 3^{3} \cdot 47 \) |
\( - 3^{7} \cdot 47 \) |
$0$ |
$2$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 5 \) |
\(1.000000\) |
\(4.110305\) |
\(0.411030\) |
$[91192,19900,603982075,1692]$ |
$[136788,779593356,5923938871071,50639487394179303,102789]$ |
$[\frac{197075993647247827966976}{423},\frac{2737061778548953841408}{141},\frac{152047414479420367856}{141}]$ |
$y^2 + (x^3 + x)y = -2x^6 - x^5 - 21x^4 - 8x^3 - 80x^2 - 16x - 103$ |
| 1269.b.102789.2 |
1269.b |
\( 3^{3} \cdot 47 \) |
\( 3^{7} \cdot 47 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(8.220609\) |
\(0.411030\) |
$[80,-140,-1027,1692]$ |
$[120,810,81,-161595,102789]$ |
$[\frac{102400000}{423},\frac{640000}{47},\frac{1600}{141}]$ |
$y^2 + xy = x^5 - x^4 + x^2 + x$ |
| 1270.a.325120.1 |
1270.a |
\( 2 \cdot 5 \cdot 127 \) |
\( 2^{9} \cdot 5 \cdot 127 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.894604\) |
\(0.473651\) |
$[239204,126763297,10436094933809,41615360]$ |
$[59801,143724846,437833820176,1381517230655315,325120]$ |
$[\frac{764790054928595680699001}{325120},\frac{15368348330455841308623}{162560},\frac{97860226229056869361}{20320}]$ |
$y^2 + (x^2 + x)y = x^5 + 17x^4 + 76x^3 + 14x^2 - 32x + 3$ |
| 1272.a.122112.1 |
1272.a |
\( 2^{3} \cdot 3 \cdot 53 \) |
\( - 2^{8} \cdot 3^{2} \cdot 53 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.397916\) |
\(0.399942\) |
$[124,-5027,-35457,15264]$ |
$[124,3992,-79504,-6448640,122112]$ |
$[\frac{114516604}{477},\frac{29731418}{477},-\frac{4775209}{477}]$ |
$y^2 + (x^2 + 1)y = 3x^5 + 4x^4 + 2x^3 - x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.093879\) |
\(7.601599\) |
\(0.237876\) |
$[4600,9904,15140164,520000]$ |
$[2300,218766,27536704,3868964111,130000]$ |
$[\frac{6436343000000}{13},\frac{266172592200}{13},1120532032]$ |
$y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13$ |
| 1311.a.814131.1 |
1311.a |
\( 3 \cdot 19 \cdot 23 \) |
\( - 3^{4} \cdot 19 \cdot 23^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.753499\) |
\(0.429797\) |
$[600,2040,860349,3256524]$ |
$[300,3410,-4761,-3264100,814131]$ |
$[\frac{30000000000}{10051},\frac{3410000000}{30153},-\frac{10000}{19}]$ |
$y^2 + xy = x^5 + 5x^4 + 5x^3 + 4x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 11 \) |
\(1.000000\) |
\(11.857814\) |
\(0.538992\) |
$[164,1441,58489,83968]$ |
$[164,160,1984,74944,671744]$ |
$[\frac{2825761}{16},\frac{8405}{8},\frac{1271}{16}]$ |
$y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$ |
