| 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 |
| 25047.a1 |
25047h1 |
25047.a |
25047h |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{16} \cdot 11^{10} \cdot 23^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$2024$ |
$4$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1562880$ |
$3.100883$ |
$-1411796061716161/31236921$ |
$1.00251$ |
$6.46238$ |
$[1, -1, 1, -62263598, 189122621438]$ |
\(y^2+xy+y=x^3-x^2-62263598x+189122621438\) |
4.2.0.a.1, 2024.4.0.? |
$[]$ |
| 25047.b1 |
25047e2 |
25047.b |
25047e |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( 3^{11} \cdot 11^{10} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$5.810405377$ |
$1$ |
|
$0$ |
$307200$ |
$2.350739$ |
$209849322390625/1882056627$ |
$0.99362$ |
$5.32719$ |
$[1, -1, 1, -1348205, -597510174]$ |
\(y^2+xy+y=x^3-x^2-1348205x-597510174\) |
2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.? |
$[(-16744/5, 312414/5)]$ |
| 25047.b2 |
25047e1 |
25047.b |
25047e |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{16} \cdot 11^{8} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$11.62081075$ |
$1$ |
|
$1$ |
$153600$ |
$2.004166$ |
$-1349232625/164333367$ |
$0.95842$ |
$4.67551$ |
$[1, -1, 1, -25070, -22211076]$ |
\(y^2+xy+y=x^3-x^2-25070x-22211076\) |
2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.? |
$[(990936/35, 928175529/35)]$ |
| 25047.c1 |
25047i6 |
25047.c |
25047i |
$6$ |
$8$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( 3^{7} \cdot 11^{7} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.56 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$16$ |
$2$ |
$0$ |
$983040$ |
$2.863361$ |
$89254274298475942657/17457$ |
$1.00726$ |
$6.60680$ |
$[1, -1, 1, -101390279, -392929443970]$ |
\(y^2+xy+y=x^3-x^2-101390279x-392929443970\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 48.48.0-48.f.1.10, 66.6.0.a.1, $\ldots$ |
$[]$ |
| 25047.c2 |
25047i4 |
25047.c |
25047i |
$6$ |
$8$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( 3^{8} \cdot 11^{8} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.24.0.3 |
2Cs |
$6072$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$2$ |
$491520$ |
$2.516788$ |
$21790813729717297/304746849$ |
$0.97272$ |
$5.78558$ |
$[1, -1, 1, -6336914, -6138291112]$ |
\(y^2+xy+y=x^3-x^2-6336914x-6138291112\) |
2.6.0.a.1, 4.24.0-4.b.1.2, 24.48.0-24.h.1.32, 88.48.0.?, 132.48.0.?, $\ldots$ |
$[]$ |
| 25047.c3 |
25047i5 |
25047.c |
25047i |
$6$ |
$8$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{7} \cdot 11^{7} \cdot 23^{8} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.46 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$2$ |
$983040$ |
$2.863361$ |
$-19989223566735457/2584262514273$ |
$0.97497$ |
$5.79697$ |
$[1, -1, 1, -6157229, -6502907914]$ |
\(y^2+xy+y=x^3-x^2-6157229x-6502907914\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 24.48.0-24.by.1.14, 88.48.0.?, $\ldots$ |
$[]$ |
| 25047.c4 |
25047i3 |
25047.c |
25047i |
$6$ |
$8$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( 3^{8} \cdot 11^{14} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.4 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$0$ |
$491520$ |
$2.516788$ |
$309368403125137/44372288367$ |
$0.95365$ |
$5.36551$ |
$[1, -1, 1, -1534424, 634866356]$ |
\(y^2+xy+y=x^3-x^2-1534424x+634866356\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0.by.2, $\ldots$ |
$[]$ |
| 25047.c5 |
25047i2 |
25047.c |
25047i |
$6$ |
$8$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( 3^{10} \cdot 11^{10} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.24 |
2Cs |
$6072$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$2$ |
$245760$ |
$2.170216$ |
$5786435182177/627352209$ |
$0.98731$ |
$4.97266$ |
$[1, -1, 1, -407309, -90094012]$ |
\(y^2+xy+y=x^3-x^2-407309x-90094012\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 24.48.0-24.h.2.9, 88.48.0.?, $\ldots$ |
$[]$ |
| 25047.c6 |
25047i1 |
25047.c |
25047i |
$6$ |
$8$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{14} \cdot 11^{8} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.4 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$1$ |
$122880$ |
$1.823641$ |
$3288008303/18259263$ |
$0.97810$ |
$4.44724$ |
$[1, -1, 1, 33736, -7001134]$ |
\(y^2+xy+y=x^3-x^2+33736x-7001134\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.8, $\ldots$ |
$[]$ |
| 25047.d1 |
25047b1 |
25047.d |
25047b |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{3} \cdot 11^{8} \cdot 23^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.16.0.1 |
|
$24$ |
$32$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$633600$ |
$2.644032$ |
$-2672676864000/78310985281$ |
$1.14869$ |
$5.43389$ |
$[0, 0, 1, -519090, -1034353708]$ |
\(y^2+y=x^3-519090x-1034353708\) |
4.4.0.a.1, 6.2.0.a.1, 8.16.0.a.1, 12.8.0.c.1, 24.32.1.e.1 |
$[]$ |
| 25047.e1 |
25047d1 |
25047.e |
25047d |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{9} \cdot 11^{8} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.16.0.1 |
|
$24$ |
$32$ |
$1$ |
$0.990728888$ |
$1$ |
|
$0$ |
$1900800$ |
$3.193340$ |
$-2672676864000/78310985281$ |
$1.14869$ |
$6.08470$ |
$[0, 0, 1, -4671810, 27927550109]$ |
\(y^2+y=x^3-4671810x+27927550109\) |
4.4.0.a.1, 6.2.0.a.1, 8.16.0.a.1, 12.8.0.c.1, 24.32.1.e.1 |
$[(44649/5, 19874732/5)]$ |
| 25047.f1 |
25047c1 |
25047.f |
25047c |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{9} \cdot 11^{2} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.16.0.1 |
|
$24$ |
$32$ |
$1$ |
$1.957906881$ |
$1$ |
|
$2$ |
$172800$ |
$1.994390$ |
$-2672676864000/78310985281$ |
$1.14869$ |
$4.66421$ |
$[0, 0, 1, -38610, -20982382]$ |
\(y^2+y=x^3-38610x-20982382\) |
4.4.0.a.1, 6.2.0.a.1, 8.16.0.a.1, 12.8.0.c.1, 24.32.1.e.1 |
$[(12978, 1478290)]$ |
| 25047.g1 |
25047a1 |
25047.g |
25047a |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{3} \cdot 11^{2} \cdot 23^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.16.0.1 |
|
$24$ |
$32$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$57600$ |
$1.445086$ |
$-2672676864000/78310985281$ |
$1.14869$ |
$4.01341$ |
$[0, 0, 1, -4290, 777125]$ |
\(y^2+y=x^3-4290x+777125\) |
4.4.0.a.1, 6.2.0.a.1, 8.16.0.a.1, 12.8.0.c.1, 24.32.1.e.1 |
$[]$ |
| 25047.h1 |
25047g1 |
25047.h |
25047g |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{16} \cdot 11^{4} \cdot 23^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$184$ |
$4$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$142080$ |
$1.901934$ |
$-1411796061716161/31236921$ |
$1.00251$ |
$5.04190$ |
$[1, -1, 0, -514575, -141950286]$ |
\(y^2+xy=x^3-x^2-514575x-141950286\) |
4.2.0.a.1, 184.4.0.? |
$[]$ |
| 25047.i1 |
25047f2 |
25047.i |
25047f |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( 3^{7} \cdot 11^{6} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$40960$ |
$1.220860$ |
$413493625/1587$ |
$0.92463$ |
$4.03013$ |
$[1, -1, 0, -16902, -838755]$ |
\(y^2+xy=x^3-x^2-16902x-838755\) |
2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.? |
$[]$ |
| 25047.i2 |
25047f1 |
25047.i |
25047f |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \cdot 23 \) |
\( - 3^{8} \cdot 11^{6} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$20480$ |
$0.874287$ |
$-15625/207$ |
$0.99061$ |
$3.33803$ |
$[1, -1, 0, -567, -25272]$ |
\(y^2+xy=x^3-x^2-567x-25272\) |
2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.? |
$[]$ |
