| 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 |
| 5776.a1 |
5776k1 |
5776.a |
5776k |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{15} \cdot 19^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.3.0.1 |
3Nn |
$456$ |
$12$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$54720$ |
$1.753960$ |
$-27/8$ |
$1.31757$ |
$5.12082$ |
$[0, 0, 0, -6859, -4952198]$ |
\(y^2=x^3-6859x-4952198\) |
3.3.0.a.1, 24.6.0.m.1, 57.6.0.a.1, 152.2.0.?, 456.12.1.? |
$[]$ |
| 5776.b1 |
5776f1 |
5776.b |
5776f |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{8} \cdot 19^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5760$ |
$0.860741$ |
$-1024/19$ |
$0.79665$ |
$3.88406$ |
$[0, 1, 0, -481, 23211]$ |
\(y^2=x^3+x^2-481x+23211\) |
38.2.0.a.1 |
$[]$ |
| 5776.c1 |
5776q3 |
5776.c |
5776q |
$3$ |
$9$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{12} \cdot 19^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$2052$ |
$1296$ |
$43$ |
$16.54388095$ |
$1$ |
|
$0$ |
$77760$ |
$2.198807$ |
$-50357871050752/19$ |
$1.10495$ |
$6.64259$ |
$[0, 1, 0, -4443669, -3606941501]$ |
\(y^2=x^3+x^2-4443669x-3606941501\) |
3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.4, 27.36.0.a.1, 36.24.0-9.a.1.3, $\ldots$ |
$[(490245949/310, 9722620510107/310)]$ |
| 5776.c2 |
5776q2 |
5776.c |
5776q |
$3$ |
$9$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{12} \cdot 19^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$2052$ |
$1296$ |
$43$ |
$5.514626985$ |
$1$ |
|
$0$ |
$25920$ |
$1.649500$ |
$-89915392/6859$ |
$1.03310$ |
$5.12876$ |
$[0, 1, 0, -53909, -5143421]$ |
\(y^2=x^3+x^2-53909x-5143421\) |
3.12.0.a.1, 9.36.0.b.1, 12.24.0-3.a.1.2, 36.72.0-9.b.1.2, 38.2.0.a.1, $\ldots$ |
$[(29309/10, 2078277/10)]$ |
| 5776.c3 |
5776q1 |
5776.c |
5776q |
$3$ |
$9$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{12} \cdot 19^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$2052$ |
$1296$ |
$43$ |
$1.838208995$ |
$1$ |
|
$0$ |
$8640$ |
$1.100193$ |
$32768/19$ |
$1.31757$ |
$4.20040$ |
$[0, 1, 0, 3851, -2781]$ |
\(y^2=x^3+x^2+3851x-2781\) |
3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.3, 27.36.0.a.1, 36.24.0-9.a.1.4, $\ldots$ |
$[(5/2, 361/2)]$ |
| 5776.d1 |
5776o2 |
5776.d |
5776o |
$2$ |
$5$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{13} \cdot 19^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$760$ |
$48$ |
$1$ |
$2.386240598$ |
$1$ |
|
$0$ |
$86400$ |
$2.183151$ |
$-37966934881/4952198$ |
$0.97714$ |
$5.83592$ |
$[0, -1, 0, -404440, -109454224]$ |
\(y^2=x^3-x^2-404440x-109454224\) |
5.12.0.a.2, 40.24.0-5.a.2.5, 152.2.0.?, 380.24.0.?, 760.48.1.? |
$[(13018/3, 1303210/3)]$ |
| 5776.d2 |
5776o1 |
5776.d |
5776o |
$2$ |
$5$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{17} \cdot 19^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$760$ |
$48$ |
$1$ |
$0.477248119$ |
$1$ |
|
$6$ |
$17280$ |
$1.378433$ |
$-1/608$ |
$1.37833$ |
$4.60076$ |
$[0, -1, 0, -120, 520816]$ |
\(y^2=x^3-x^2-120x+520816\) |
5.12.0.a.1, 40.24.0-5.a.1.5, 152.2.0.?, 380.24.0.?, 760.48.1.? |
$[(-6, 722)]$ |
| 5776.e1 |
5776b1 |
5776.e |
5776b |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{11} \cdot 19^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
8.2.0.1 |
|
$8$ |
$2$ |
$0$ |
$0.224869741$ |
$1$ |
|
$6$ |
$2016$ |
$0.309282$ |
$-722$ |
$0.85758$ |
$3.14106$ |
$[0, -1, 0, -120, 976]$ |
\(y^2=x^3-x^2-120x+976\) |
8.2.0.a.1 |
$[(-6, 38)]$ |
| 5776.f1 |
5776n1 |
5776.f |
5776n |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
2.2.0.1, 5.5.0.1 |
2Cn, 5S4 |
$380$ |
$60$ |
$2$ |
$0.768303250$ |
$1$ |
|
$2$ |
$216$ |
$-0.562854$ |
$4864$ |
$0.64811$ |
$1.98016$ |
$[0, -1, 0, -6, 7]$ |
\(y^2=x^3-x^2-6x+7\) |
2.2.0.a.1, 5.5.0.a.1, 10.10.0.a.1, 38.6.0.a.1, 76.12.0.?, $\ldots$ |
$[(1, 1)]$ |
| 5776.g1 |
5776i2 |
5776.g |
5776i |
$2$ |
$3$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{21} \cdot 19^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 9.12.0.2 |
3B |
$1368$ |
$144$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$49248$ |
$2.061771$ |
$-246579625/512$ |
$0.97319$ |
$5.91125$ |
$[0, -1, 0, -537288, 152036848]$ |
\(y^2=x^3-x^2-537288x+152036848\) |
3.4.0.a.1, 8.2.0.a.1, 9.12.0.b.1, 12.8.0-3.a.1.2, 24.16.0-24.a.1.7, $\ldots$ |
$[]$ |
| 5776.g2 |
5776i1 |
5776.g |
5776i |
$2$ |
$3$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{15} \cdot 19^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 9.12.0.2 |
3B |
$1368$ |
$144$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$16416$ |
$1.512465$ |
$2375/8$ |
$0.86529$ |
$4.75889$ |
$[0, -1, 0, 11432, 1029104]$ |
\(y^2=x^3-x^2+11432x+1029104\) |
3.4.0.a.1, 8.2.0.a.1, 9.12.0.b.1, 12.8.0-3.a.1.1, 24.16.0-24.a.1.5, $\ldots$ |
$[]$ |
| 5776.h1 |
5776a1 |
5776.h |
5776a |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.4.0.2, 5.5.0.1 |
2Cn, 5S4 |
$380$ |
$60$ |
$2$ |
$16.15011553$ |
$1$ |
|
$0$ |
$19152$ |
$1.508987$ |
$1462911232$ |
$0.97310$ |
$5.47619$ |
$[0, -1, 0, -153184, -23025409]$ |
\(y^2=x^3-x^2-153184x-23025409\) |
2.2.0.a.1, 4.4.0-2.a.1.1, 5.5.0.a.1, 10.10.0.a.1, 20.20.0-10.a.1.2, $\ldots$ |
$[(-167955205/863, 1228756067/863)]$ |
| 5776.i1 |
5776g2 |
5776.i |
5776g |
$2$ |
$19$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{12} \cdot 19^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-19})$ |
$-19$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$27360$ |
$1.815218$ |
$-884736$ |
$1.31757$ |
$5.60098$ |
$[0, 0, 0, -219488, 39617584]$ |
\(y^2=x^3-219488x+39617584\) |
|
$[]$ |
| 5776.i2 |
5776g1 |
5776.i |
5776g |
$2$ |
$19$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{12} \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-19})$ |
$-19$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$1440$ |
$0.342999$ |
$-884736$ |
$1.31757$ |
$3.56130$ |
$[0, 0, 0, -608, -5776]$ |
\(y^2=x^3-608x-5776\) |
|
$[]$ |
| 5776.j1 |
5776e1 |
5776.j |
5776e |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{11} \cdot 19^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
8.2.0.1 |
|
$8$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$38304$ |
$1.781502$ |
$-722$ |
$0.85758$ |
$5.18075$ |
$[0, 1, 0, -43440, -6433996]$ |
\(y^2=x^3+x^2-43440x-6433996\) |
8.2.0.a.1 |
$[]$ |
| 5776.k1 |
5776h1 |
5776.k |
5776h |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.4.0.2, 5.5.0.1 |
2Cn, 5S4 |
$380$ |
$60$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$4104$ |
$0.909366$ |
$4864$ |
$0.64811$ |
$4.01984$ |
$[0, 1, 0, -2286, -34549]$ |
\(y^2=x^3+x^2-2286x-34549\) |
2.2.0.a.1, 4.4.0-2.a.1.1, 5.5.0.a.1, 10.10.0.a.1, 20.20.0-10.a.1.2, $\ldots$ |
$[]$ |
| 5776.l1 |
5776c1 |
5776.l |
5776c |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{11} \cdot 19^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$152$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5760$ |
$1.055040$ |
$-31250/19$ |
$0.89957$ |
$4.19781$ |
$[0, 1, 0, -3008, -91948]$ |
\(y^2=x^3+x^2-3008x-91948\) |
152.2.0.? |
$[]$ |
| 5776.m1 |
5776l3 |
5776.m |
5776l |
$3$ |
$9$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{39} \cdot 19^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$8.273244123$ |
$1$ |
|
$0$ |
$155520$ |
$2.650536$ |
$-69173457625/2550136832$ |
$1.05462$ |
$6.36314$ |
$[0, 1, 0, -493968, -1075051756]$ |
\(y^2=x^3+x^2-493968x-1075051756\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.7, 27.36.0.a.1, 72.24.0.?, $\ldots$ |
$[(25942738/93, 125744906240/93)]$ |
| 5776.m2 |
5776l1 |
5776.m |
5776l |
$3$ |
$9$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{15} \cdot 19^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$0.919249347$ |
$1$ |
|
$4$ |
$17280$ |
$1.551924$ |
$-413493625/152$ |
$0.93281$ |
$5.29070$ |
$[0, 1, 0, -89648, 10304852]$ |
\(y^2=x^3+x^2-89648x+10304852\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.8, 27.36.0.a.1, 72.24.0.?, $\ldots$ |
$[(386, 5776)]$ |
| 5776.m3 |
5776l2 |
5776.m |
5776l |
$3$ |
$9$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{21} \cdot 19^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$4104$ |
$1296$ |
$43$ |
$2.757748041$ |
$1$ |
|
$0$ |
$51840$ |
$2.101231$ |
$94196375/3511808$ |
$1.01875$ |
$5.59895$ |
$[0, 1, 0, 54752, 39288820]$ |
\(y^2=x^3+x^2+54752x+39288820\) |
3.12.0.a.1, 9.36.0.b.1, 24.24.0-3.a.1.4, 72.72.0.?, 152.2.0.?, $\ldots$ |
$[(2410/3, 231040/3)]$ |
| 5776.n1 |
5776m2 |
5776.n |
5776m |
$2$ |
$3$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{21} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 9.12.0.2 |
3B |
$1368$ |
$144$ |
$2$ |
$6.283698464$ |
$1$ |
|
$0$ |
$2592$ |
$0.589552$ |
$-246579625/512$ |
$0.97319$ |
$3.87156$ |
$[0, 1, 0, -1488, -22636]$ |
\(y^2=x^3+x^2-1488x-22636\) |
3.4.0.a.1, 8.2.0.a.1, 9.12.0.b.1, 24.8.0.a.1, 72.24.0.?, $\ldots$ |
$[(868/3, 23230/3)]$ |
| 5776.n2 |
5776m1 |
5776.n |
5776m |
$2$ |
$3$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{15} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 9.12.0.2 |
3B |
$1368$ |
$144$ |
$2$ |
$2.094566154$ |
$1$ |
|
$2$ |
$864$ |
$0.040246$ |
$2375/8$ |
$0.86529$ |
$2.71920$ |
$[0, 1, 0, 32, -140]$ |
\(y^2=x^3+x^2+32x-140\) |
3.4.0.a.1, 8.2.0.a.1, 9.12.0.b.1, 24.8.0.a.1, 72.24.0.?, $\ldots$ |
$[(12, 46)]$ |
| 5776.o1 |
5776d1 |
5776.o |
5776d |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
2.2.0.1, 5.5.0.1 |
2Cn, 5S4 |
$380$ |
$60$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$1008$ |
$0.036767$ |
$1462911232$ |
$0.97310$ |
$3.43650$ |
$[0, 1, 0, -424, 3223]$ |
\(y^2=x^3+x^2-424x+3223\) |
2.2.0.a.1, 5.5.0.a.1, 10.10.0.a.1, 38.6.0.a.1, 76.12.0.?, $\ldots$ |
$[]$ |
| 5776.p1 |
5776p1 |
5776.p |
5776p |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{8} \cdot 19^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$5.276507669$ |
$1$ |
|
$2$ |
$8640$ |
$1.031288$ |
$-4194304/19$ |
$1.07903$ |
$4.44138$ |
$[0, -1, 0, -7701, -258583]$ |
\(y^2=x^3-x^2-7701x-258583\) |
38.2.0.a.1 |
$[(341, 6054)]$ |
| 5776.q1 |
5776j1 |
5776.q |
5776j |
$1$ |
$1$ |
\( 2^{4} \cdot 19^{2} \) |
\( - 2^{15} \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.3.0.1 |
3Nn |
$456$ |
$12$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$2880$ |
$0.281740$ |
$-27/8$ |
$1.31757$ |
$3.08114$ |
$[0, 0, 0, -19, 722]$ |
\(y^2=x^3-19x+722\) |
3.3.0.a.1, 24.6.0.m.1, 57.6.0.a.1, 152.2.0.?, 456.12.1.? |
$[]$ |
