Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
30030.bt5 |
30030bt4 |
30030.bt |
30030bt |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{4} \cdot 13^{12} \) |
$1$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
4.12.0.8, 3.8.0.1 |
2B, 3B.1.1 |
$24024$ |
$384$ |
$5$ |
$6.540224643$ |
$1$ |
|
$6$ |
$3096576$ |
$2.994370$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, 0, 0, -12369181, 15826636745]$ |
\(y^2+xy=x^3-12369181x+15826636745\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.12.0-4.c.1.2, 6.24.0-6.a.1.4, 12.96.0-12.c.3.7, $\ldots$ |
$[(2444, 12785)]$ |
90090.ce5 |
90090cd4 |
90090.ce |
90090cd |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \) |
\( 2^{3} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{4} \cdot 13^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$24024$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$24772608$ |
$3.543674$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, -1, 0, -111322629, -427319192115]$ |
\(y^2+xy=x^3-x^2-111322629x-427319192115\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 12.96.0-12.c.3.3, $\ldots$ |
$[]$ |
150150.e5 |
150150gn5 |
150150.e |
150150gn |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{8} \cdot 7 \cdot 11^{4} \cdot 13^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$120120$ |
$384$ |
$5$ |
$7.600324862$ |
$4$ |
$2$ |
$2$ |
$74317824$ |
$3.799088$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, 1, 0, -309229525, 1978329593125]$ |
\(y^2+xy=x^3+x^2-309229525x+1978329593125\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(-6841, 1946015)]$ |
210210.dn5 |
210210cg4 |
210210.dn |
210210cg |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11^{4} \cdot 13^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$24024$ |
$384$ |
$5$ |
$1$ |
$16$ |
$2$ |
$0$ |
$148635648$ |
$3.967323$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, 1, 1, -606089870, -5429142493405]$ |
\(y^2+xy+y=x^3+x^2-606089870x-5429142493405\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
240240.bc5 |
240240bc4 |
240240.bc |
240240bc |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \) |
\( 2^{15} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{4} \cdot 13^{12} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.7, 3.4.0.1 |
2B, 3B |
$24024$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$3$ |
$74317824$ |
$3.687515$ |
$209289070072300727183442769/12893854589717635333800$ |
$[0, -1, 0, -197906896, -1012904751680]$ |
\(y^2=x^3-x^2-197906896x-1012904751680\) |
2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.c.1.1, 6.12.0.a.1, 12.96.0-12.c.3.8, $\ldots$ |
$[]$ |
330330.br5 |
330330br4 |
330330.br |
330330br |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{10} \cdot 13^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$24024$ |
$384$ |
$5$ |
$22.89827619$ |
$1$ |
|
$0$ |
$371589120$ |
$4.193314$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, 0, 1, -1496670904, -21066750178498]$ |
\(y^2+xy+y=x^3-1496670904x-21066750178498\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(17963748484/125, 2405158923351898/125)]$ |
390390.bz5 |
390390bz5 |
390390.bz |
390390bz |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{4} \cdot 13^{18} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$24024$ |
$384$ |
$5$ |
$1$ |
$4$ |
$2$ |
$0$ |
$520224768$ |
$4.276848$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, 0, 1, -2090391593, 34773211320356]$ |
\(y^2+xy+y=x^3-2090391593x+34773211320356\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
450450.hc5 |
450450hc4 |
450450.hc |
450450hc |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( 2^{3} \cdot 3^{9} \cdot 5^{8} \cdot 7 \cdot 11^{4} \cdot 13^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$120120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$594542592$ |
$4.348396$ |
$209289070072300727183442769/12893854589717635333800$ |
$[1, -1, 1, -2783065730, -53417682080103]$ |
\(y^2+xy+y=x^3-x^2-2783065730x-53417682080103\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |