| 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 |
| 6075.a.18225.1 |
6075.a |
\( 3^{5} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.574664\) |
\(0.865259\) |
$[164,2745,106365,-9600]$ |
$[123,-399,-409,-52377,-18225]$ |
$[-\frac{115856201}{75},\frac{9166493}{225},\frac{687529}{2025}]$ |
$y^2 + (x^3 + 1)y = x^3 + 1$ |
| 15552.c.746496.1 |
15552.c |
\( 2^{6} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(8.616344\) |
\(0.957372\) |
$[142,1368,47940,-12]$ |
$[852,-2586,-2596,-2224797,-746496]$ |
$[-\frac{1804229351}{3},\frac{154259641}{72},\frac{3271609}{1296}]$ |
$y^2 + x^3y = 3x^3 + 8$ |
| 18225.a.18225.1 |
18225.a |
\( 3^{6} \cdot 5^{2} \) |
\( - 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.687921\) |
\(16.468178\) |
\(1.258756\) |
$[196,1305,73965,9600]$ |
$[147,411,-401,-56967,18225]$ |
$[\frac{282475249}{75},\frac{16117913}{225},-\frac{962801}{2025}]$ |
$y^2 + (x^3 + 1)y = 1$ |
| 46656.c.93312.1 |
46656.c |
\( 2^{6} \cdot 3^{6} \) |
\( 2^{7} \cdot 3^{6} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.8640.14 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.664878\) |
\(8.473201\) |
\(1.877882\) |
$[44,9,357,48]$ |
$[132,672,-1264,-154608,93312]$ |
$[\frac{1288408}{3},\frac{149072}{9},-\frac{19118}{81}]$ |
$y^2 + x^3y = x^3 - 1$ |
| 62208.n.746496.1 |
62208.n |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(8.616344\) |
\(1.436057\) |
$[142,1368,47940,-12]$ |
$[852,-2586,-2596,-2224797,-746496]$ |
$[-\frac{1804229351}{3},\frac{154259641}{72},\frac{3271609}{1296}]$ |
$y^2 = x^6 - 3x^3 + 2$ |
| 72900.a.291600.1 |
72900.a |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.2880.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.563877\) |
\(10.315182\) |
\(1.938833\) |
$[184,1845,87015,150]$ |
$[552,1626,-1616,-883977,291600]$ |
$[\frac{13181630464}{75},\frac{211024448}{225},-\frac{3419456}{2025}]$ |
$y^2 + y = x^6 - 2x^3 + 1$ |
| 72900.b.291600.1 |
72900.b |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.20.3, 3.8640.7 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.315182\) |
\(1.146131\) |
$[184,1845,87015,150]$ |
$[552,1626,-1616,-883977,291600]$ |
$[\frac{13181630464}{75},\frac{211024448}{225},-\frac{3419456}{2025}]$ |
$y^2 + x^3y = 2x^3 + 5$ |
| 104976.a.104976.1 |
104976.a |
\( 2^{4} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{8} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.40.1, 3.960.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.539918\) |
\(3.982188\) |
\(2.150055\) |
$[104,837,21105,-54]$ |
$[312,-966,-976,-309417,-104976]$ |
$[-\frac{760408064}{27},\frac{22637888}{81},\frac{659776}{729}]$ |
$y^2 + y = -x^6 - 2x^3 - 1$ |
| 104976.b.104976.1 |
104976.b |
\( 2^{4} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{8} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.40.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.946565\) |
\(1.327396\) |
$[104,837,21105,-54]$ |
$[312,-966,-976,-309417,-104976]$ |
$[-\frac{760408064}{27},\frac{22637888}{81},\frac{659776}{729}]$ |
$y^2 + x^3y = 2x^3 + 3$ |
| 107163.a.321489.1 |
107163.a |
\( 3^{7} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$1$ |
$1$ |
2.120.1, 3.960.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.321348\) |
\(3.316200\) |
\(2.190927\) |
$[740,38745,7033005,-169344]$ |
$[555,-1695,-1705,-954825,-321489]$ |
$[-\frac{216699865625}{1323},\frac{3577368125}{3969},\frac{58353625}{35721}]$ |
$y^2 + (x^3 + 1)y = -x^6 + 2x^3 - 2$ |
| 123201.a.123201.1 |
123201.a |
\( 3^{6} \cdot 13^{2} \) |
\( - 3^{6} \cdot 13^{2} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.20.3, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.975116\) |
\(1.330568\) |
$[484,11817,1489605,64896]$ |
$[363,1059,-1049,-375567,123201]$ |
$[\frac{25937424601}{507},\frac{625361033}{1521},-\frac{15358409}{13689}]$ |
$y^2 + (x^3 + 1)y = x^3 + 3$ |
| 139968.b.839808.1 |
139968.b |
\( 2^{6} \cdot 3^{7} \) |
\( - 2^{7} \cdot 3^{8} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.960.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.364886\) |
\(10.972817\) |
\(2.669218\) |
$[116,513,16623,432]$ |
$[348,1968,-3856,-1303728,839808]$ |
$[\frac{164089192}{27},\frac{7999592}{81},-\frac{405362}{729}]$ |
$y^2 + x^3y = x^3 + 3$ |
| 142884.a.285768.1 |
142884.a |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 7^{2} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.20.3, 3.960.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.453892\) |
\(2.484631\) |
$[284,1953,181167,150528]$ |
$[213,1158,-2236,-454308,285768]$ |
$[\frac{1804229351}{1176},\frac{69076823}{1764},-\frac{2817919}{7938}]$ |
$y^2 + (x^3 + 1)y = -2$ |
| 248832.d.746496.1 |
248832.d |
\( 2^{10} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$1$ |
$1$ |
2.120.1, 3.1440.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(2.872115\) |
\(1.436057\) |
$[142,1368,47940,-12]$ |
$[852,-2586,-2596,-2224797,-746496]$ |
$[-\frac{1804229351}{3},\frac{154259641}{72},\frac{3271609}{1296}]$ |
$y^2 = -x^6 - 3x^3 - 2$ |
| 321489.a.321489.1 |
321489.a |
\( 3^{8} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{2} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.40.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.948599\) |
\(1.105400\) |
$[740,38745,7033005,-169344]$ |
$[555,-1695,-1705,-954825,-321489]$ |
$[-\frac{216699865625}{1323},\frac{3577368125}{3969},\frac{58353625}{35721}]$ |
$y^2 + (x^3 + 1)y = 2x^3 + 5$ |
| 419904.e.839808.1 |
419904.e |
\( 2^{6} \cdot 3^{8} \) |
\( - 2^{7} \cdot 3^{8} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$0$ |
$0$ |
2.20.3, 3.2880.7 |
|
✓ |
$1$ |
\( 1 \) |
\(1.013495\) |
\(3.657606\) |
\(3.706965\) |
$[116,513,16623,432]$ |
$[348,1968,-3856,-1303728,839808]$ |
$[\frac{164089192}{27},\frac{7999592}{81},-\frac{405362}{729}]$ |
$y^2 + y = -x^6 - x^3 - 1$ |
| 613089.b.613089.1 |
613089.b |
\( 3^{6} \cdot 29^{2} \) |
\( - 3^{6} \cdot 29^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.20.3, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(3.976933\) |
\(9.045652\) |
\(3.997106\) |
$[1060,63945,17229045,322944]$ |
$[795,2355,-2345,-1852575,613089]$ |
$[\frac{1306860915625}{2523},\frac{14608555625}{7569},-\frac{164677625}{68121}]$ |
$y^2 + (x^3 + 1)y = 2x^3 + 7$ |
