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 |
8349.a1 |
8349d2 |
8349.a |
8349d |
$2$ |
$2$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( 3 \cdot 11^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$1.262325511$ |
$1$ |
|
$2$ |
$5120$ |
$0.671554$ |
$413493625/1587$ |
$[1, 0, 0, -1878, 31065]$ |
\(y^2+xy=x^3-1878x+31065\) |
2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.? |
$[(-1, 182)]$ |
8349.a2 |
8349d1 |
8349.a |
8349d |
$2$ |
$2$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( - 3^{2} \cdot 11^{6} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$2.524651022$ |
$1$ |
|
$3$ |
$2560$ |
$0.324981$ |
$-15625/207$ |
$[1, 0, 0, -63, 936]$ |
\(y^2+xy=x^3-63x+936\) |
2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.? |
$[(15, 51)]$ |
8349.b1 |
8349e1 |
8349.b |
8349e |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( - 3^{10} \cdot 11^{4} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$552$ |
$4$ |
$0$ |
$0.201343310$ |
$1$ |
|
$8$ |
$17760$ |
$1.352629$ |
$-1411796061716161/31236921$ |
$[1, 0, 0, -57175, 5257418]$ |
\(y^2+xy=x^3-57175x+5257418\) |
4.2.0.a.1, 552.4.0.? |
$[(143, 32)]$ |
8349.c1 |
8349a2 |
8349.c |
8349a |
$2$ |
$2$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( 3^{5} \cdot 11^{10} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$4.928290454$ |
$1$ |
|
$0$ |
$38400$ |
$1.801434$ |
$209849322390625/1882056627$ |
$[1, 1, 0, -149800, 22080073]$ |
\(y^2+xy=x^3+x^2-149800x+22080073\) |
2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.? |
$[(11712/7, -27077/7)]$ |
8349.c2 |
8349a1 |
8349.c |
8349a |
$2$ |
$2$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( - 3^{10} \cdot 11^{8} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$9.856580909$ |
$1$ |
|
$1$ |
$19200$ |
$1.454861$ |
$-1349232625/164333367$ |
$[1, 1, 0, -2785, 821704]$ |
\(y^2+xy=x^3+x^2-2785x+821704\) |
2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.? |
$[(297259/2, 161774021/2)]$ |
8349.d1 |
8349c5 |
8349.d |
8349c |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( 3 \cdot 11^{7} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.14 |
2B |
$12144$ |
$192$ |
$1$ |
$5.632347455$ |
$1$ |
|
$2$ |
$122880$ |
$2.314056$ |
$89254274298475942657/17457$ |
$[1, 0, 1, -11265587, 14552942369]$ |
\(y^2+xy+y=x^3-11265587x+14552942369\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0-8.n.1.6, $\ldots$ |
$[(-3631, 88935)]$ |
8349.d2 |
8349c4 |
8349.d |
8349c |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( 3^{2} \cdot 11^{8} \cdot 23^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.17 |
2Cs |
$6072$ |
$192$ |
$1$ |
$11.26469491$ |
$1$ |
|
$2$ |
$61440$ |
$1.967482$ |
$21790813729717297/304746849$ |
$[1, 0, 1, -704102, 227344115]$ |
\(y^2+xy+y=x^3-704102x+227344115\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 12.24.0-4.b.1.2, 24.48.0-24.h.1.27, $\ldots$ |
$[(1028103/46, -21506957/46)]$ |
8349.d3 |
8349c6 |
8349.d |
8349c |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( - 3 \cdot 11^{7} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.89 |
2B |
$12144$ |
$192$ |
$1$ |
$22.52938982$ |
$1$ |
|
$0$ |
$122880$ |
$2.314056$ |
$-19989223566735457/2584262514273$ |
$[1, 0, 1, -684137, 240848441]$ |
\(y^2+xy+y=x^3-684137x+240848441\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0-4.c.1.2, 24.48.0-24.by.1.10, $\ldots$ |
$[(-3877585361/2070, 100799732481823/2070)]$ |
8349.d4 |
8349c3 |
8349.d |
8349c |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( 3^{2} \cdot 11^{14} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.3 |
2B |
$12144$ |
$192$ |
$1$ |
$11.26469491$ |
$1$ |
|
$0$ |
$61440$ |
$1.967482$ |
$309368403125137/44372288367$ |
$[1, 0, 1, -170492, -23513569]$ |
\(y^2+xy+y=x^3-170492x-23513569\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.5, 24.24.0.by.2, $\ldots$ |
$[(134199/2, 49023605/2)]$ |
8349.d5 |
8349c2 |
8349.d |
8349c |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( 3^{4} \cdot 11^{10} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.9 |
2Cs |
$6072$ |
$192$ |
$1$ |
$5.632347455$ |
$1$ |
|
$4$ |
$30720$ |
$1.620909$ |
$5786435182177/627352209$ |
$[1, 0, 1, -45257, 3336815]$ |
\(y^2+xy+y=x^3-45257x+3336815\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 24.48.0-24.h.2.14, 44.24.0-4.b.1.3, $\ldots$ |
$[(615/2, 485/2)]$ |
8349.d6 |
8349c1 |
8349.d |
8349c |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( - 3^{8} \cdot 11^{8} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.87 |
2B |
$12144$ |
$192$ |
$1$ |
$2.816173727$ |
$1$ |
|
$3$ |
$15360$ |
$1.274334$ |
$3288008303/18259263$ |
$[1, 0, 1, 3748, 259301]$ |
\(y^2+xy+y=x^3+3748x+259301\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 44.12.0-4.c.1.2, 46.6.0.a.1, $\ldots$ |
$[(63, 832)]$ |
8349.e1 |
8349b1 |
8349.e |
8349b |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 23 \) |
\( - 3^{10} \cdot 11^{10} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$6072$ |
$4$ |
$0$ |
$6.925219628$ |
$1$ |
|
$2$ |
$195360$ |
$2.551575$ |
$-1411796061716161/31236921$ |
$[1, 0, 1, -6918178, -7004541535]$ |
\(y^2+xy+y=x^3-6918178x-7004541535\) |
4.2.0.a.1, 6072.4.0.? |
$[(26785, 4348304)]$ |