| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(7.977095\) |
\(0.221586\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 + 4x^4 + 4x^2 + 1$ |
| 476.a.952.1 |
476.a |
\( 2^{2} \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 7 \cdot 17 \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(26.722339\) |
\(0.247429\) |
$[7340,1042345,2905273355,121856]$ |
$[1835,96870,-3910340,-4139817700,952]$ |
$[20805604708146875/952,299272981175625/476,-27661753375/2]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$ |
| 1180.a.18880.1 |
1180.a |
\( 2^{2} \cdot 5 \cdot 59 \) |
\( - 2^{6} \cdot 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/18\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(24.170512\) |
\(0.447602\) |
$[916,23257,5960477,-2416640]$ |
$[229,1216,6656,11392,-18880]$ |
$[-629763392149/18880,-228170791/295,-5453864/295]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 + 2x$ |
| 1728.a.27648.1 |
1728.a |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{10} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/18\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(22.164198\) |
\(0.615672\) |
$[324,2259,289890,3456]$ |
$[324,2868,-43408,-5572404,27648]$ |
$[129140163,14112711/4,-659259/4]$ |
$y^2 + (x + 1)y = 3x^6 - 3x^4 - x^3$ |
| 2320.b.185600.1 |
2320.b |
\( 2^{4} \cdot 5 \cdot 29 \) |
\( 2^{8} \cdot 5^{2} \cdot 29 \) |
$0$ |
$1$ |
$\Z/18\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3^{2} \) |
\(1.000000\) |
\(13.382897\) |
\(0.743494\) |
$[208,2248,126644,-742400]$ |
$[104,76,-644,-18188,-185600]$ |
$[-47525504/725,-333944/725,27209/725]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 - x + 1$ |
| 2700.a.81000.1 |
2700.a |
\( 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{4} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3^{2} \) |
\(1.000000\) |
\(13.310902\) |
\(0.739495\) |
$[71148,84879081,2273663276523,10368000]$ |
$[17787,9645762,-1078366500,-28055407374036,81000]$ |
$[21980041417758601947/1000,335065445635338803/500,-8423969286117/2]$ |
$y^2 + (x^3 + 1)y = 5x^5 + 26x^4 + 12x^3 + 26x^2 + 5x$ |
| 2700.b.324000.1 |
2700.b |
\( 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{5} \cdot 3^{4} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3^{2} \) |
\(1.000000\) |
\(8.245576\) |
\(0.458088\) |
$[3612,34209,40180527,41472000]$ |
$[903,32550,1503900,74629800,324000]$ |
$[7412312704503/4000,5917785517/80,151394271/40]$ |
$y^2 + (x^2 + x)y = x^6 + x^5 + 4x^4 + 2x^3 + 4x^2 + x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3^{3} \) |
\(1.000000\) |
\(9.213670\) |
\(0.767806\) |
$[330,180,17190,567]$ |
$[660,17670,631260,26100675,145152]$ |
$[6039412500/7,489974375/14,7577625/4]$ |
$y^2 = x^6 - 2x^5 + 5x^4 - 5x^3 + 5x^2 - 2x + 1$ |
| 4400.b.352000.1 |
4400.b |
\( 2^{4} \cdot 5^{2} \cdot 11 \) |
\( - 2^{8} \cdot 5^{3} \cdot 11 \) |
$1$ |
$2$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.90.1, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{3} \) |
\(0.365679\) |
\(17.627207\) |
\(0.537158\) |
$[154,1876,128326,1375]$ |
$[308,-1050,-416900,-32376925,352000]$ |
$[984285148/125,-871563/10,-2247091/20]$ |
$y^2 = x^6 - 2x^4 - 3x^3 + x^2 + 3x + 1$ |
