| 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 |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 5491.a1 |
5491b1 |
5491.a |
5491b |
$1$ |
$1$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{11} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$646$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$40320$ |
$1.530354$ |
$-10764582912/26977283$ |
$0.97754$ |
$4.85111$ |
$[0, 0, 1, -13294, 1362129]$ |
\(y^2+y=x^3-13294x+1362129\) |
646.2.0.? |
$[]$ |
| 5491.b1 |
5491a3 |
5491.b |
5491a |
$3$ |
$9$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{6} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$17442$ |
$1296$ |
$43$ |
$1$ |
$9$ |
$3$ |
$0$ |
$15120$ |
$1.450047$ |
$-50357871050752/19$ |
$1.10495$ |
$5.63816$ |
$[0, -1, 1, -222337, -40278040]$ |
\(y^2+y=x^3-x^2-222337x-40278040\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 51.8.0-3.a.1.1, $\ldots$ |
$[]$ |
| 5491.b2 |
5491a2 |
5491.b |
5491a |
$3$ |
$9$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{6} \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$17442$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$0$ |
$5040$ |
$0.900740$ |
$-89915392/6859$ |
$1.03310$ |
$4.11544$ |
$[0, -1, 1, -2697, -56465]$ |
\(y^2+y=x^3-x^2-2697x-56465\) |
3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 51.24.0-3.a.1.1, 114.24.1.?, $\ldots$ |
$[]$ |
| 5491.b3 |
5491a1 |
5491.b |
5491a |
$3$ |
$9$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{6} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$17442$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$0$ |
$1680$ |
$0.351434$ |
$32768/19$ |
$1.31757$ |
$3.18162$ |
$[0, -1, 1, 193, -110]$ |
\(y^2+y=x^3-x^2+193x-110\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 51.8.0-3.a.1.2, $\ldots$ |
$[]$ |
| 5491.c1 |
5491d2 |
5491.c |
5491d |
$2$ |
$2$ |
\( 17^{2} \cdot 19 \) |
\( 17^{3} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.2 |
2B |
$2584$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$3328$ |
$0.380206$ |
$234885113/130321$ |
$0.93471$ |
$3.22549$ |
$[1, 0, 1, -219, -271]$ |
\(y^2+xy+y=x^3-219x-271\) |
2.3.0.a.1, 4.6.0.d.1, 34.6.0.a.1, 68.24.0-68.i.1.1, 152.12.0.?, $\ldots$ |
$[]$ |
| 5491.c2 |
5491d1 |
5491.c |
5491d |
$2$ |
$2$ |
\( 17^{2} \cdot 19 \) |
\( 17^{3} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.2 |
2B |
$2584$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$1664$ |
$0.033632$ |
$53582633/361$ |
$0.84837$ |
$3.05386$ |
$[1, 0, 1, -134, 579]$ |
\(y^2+xy+y=x^3-134x+579\) |
2.3.0.a.1, 4.6.0.d.1, 34.6.0.a.1, 68.24.0-68.i.1.2, 152.12.0.?, $\ldots$ |
$[]$ |
| 5491.d1 |
5491c2 |
5491.d |
5491c |
$2$ |
$2$ |
\( 17^{2} \cdot 19 \) |
\( 17^{9} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.2 |
2B |
$2584$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$56576$ |
$1.796812$ |
$234885113/130321$ |
$0.93471$ |
$5.19965$ |
$[1, 1, 0, -63152, -1267045]$ |
\(y^2+xy=x^3+x^2-63152x-1267045\) |
2.3.0.a.1, 4.6.0.d.1, 34.6.0.a.1, 68.24.0-68.i.1.1, 152.12.0.?, $\ldots$ |
$[]$ |
| 5491.d2 |
5491c1 |
5491.d |
5491c |
$2$ |
$2$ |
\( 17^{2} \cdot 19 \) |
\( 17^{9} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.2 |
2B |
$2584$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$28288$ |
$1.450239$ |
$53582633/361$ |
$0.84837$ |
$5.02803$ |
$[1, 1, 0, -38587, 2884440]$ |
\(y^2+xy=x^3+x^2-38587x+2884440\) |
2.3.0.a.1, 4.6.0.d.1, 34.6.0.a.1, 68.24.0-68.i.1.2, 152.12.0.?, $\ldots$ |
$[]$ |
| 5491.e1 |
5491f1 |
5491.e |
5491f |
$2$ |
$5$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{9} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3230$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$14144$ |
$1.233160$ |
$-5451776/19$ |
$0.79821$ |
$4.76333$ |
$[0, -1, 1, -18014, 939429]$ |
\(y^2+y=x^3-x^2-18014x+939429\) |
5.6.0.a.1, 85.24.0.?, 190.12.0.?, 646.2.0.?, 3230.48.1.? |
$[]$ |
| 5491.e2 |
5491f2 |
5491.e |
5491f |
$2$ |
$5$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{9} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3230$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$70720$ |
$2.037880$ |
$2019487744/2476099$ |
$0.93786$ |
$5.46254$ |
$[0, -1, 1, 129376, -18987699]$ |
\(y^2+y=x^3-x^2+129376x-18987699\) |
5.6.0.a.1, 85.24.0.?, 190.12.0.?, 646.2.0.?, 3230.48.1.? |
$[]$ |
| 5491.f1 |
5491e1 |
5491.f |
5491e |
$2$ |
$5$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{3} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3230$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$832$ |
$-0.183446$ |
$-5451776/19$ |
$0.79821$ |
$2.78916$ |
$[0, 1, 1, -62, 169]$ |
\(y^2+y=x^3+x^2-62x+169\) |
5.6.0.a.1, 85.24.0.?, 190.12.0.?, 646.2.0.?, 3230.48.1.? |
$[]$ |
| 5491.f2 |
5491e2 |
5491.f |
5491e |
$2$ |
$5$ |
\( 17^{2} \cdot 19 \) |
\( - 17^{3} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3230$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$4160$ |
$0.621273$ |
$2019487744/2476099$ |
$0.93786$ |
$3.48837$ |
$[0, 1, 1, 448, -3707]$ |
\(y^2+y=x^3+x^2+448x-3707\) |
5.6.0.a.1, 85.24.0.?, 190.12.0.?, 646.2.0.?, 3230.48.1.? |
$[]$ |
