| 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 |
| 9537.a1 |
9537e1 |
9537.a |
9537e |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{4} \cdot 11 \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$374$ |
$2$ |
$0$ |
$0.259735585$ |
$1$ |
|
$6$ |
$18432$ |
$0.937770$ |
$-64000000/15147$ |
$0.90115$ |
$3.85428$ |
$[0, -1, 1, -2408, 54800]$ |
\(y^2+y=x^3-x^2-2408x+54800\) |
374.2.0.? |
$[(125, 1300)]$ |
| 9537.b1 |
9537c3 |
9537.b |
9537c |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( 3 \cdot 11 \cdot 17^{10} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$4488$ |
$48$ |
$0$ |
$5.661432055$ |
$1$ |
|
$0$ |
$36864$ |
$1.507664$ |
$666940371553/2756193$ |
$0.98070$ |
$4.82654$ |
$[1, 1, 1, -52604, -4649140]$ |
\(y^2+xy+y=x^3+x^2-52604x-4649140\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 66.6.0.a.1, 68.12.0-4.c.1.1, $\ldots$ |
$[(-541/2, 1493/2)]$ |
| 9537.b2 |
9537c2 |
9537.b |
9537c |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( 3^{2} \cdot 11^{2} \cdot 17^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$2244$ |
$48$ |
$0$ |
$2.830716027$ |
$1$ |
|
$6$ |
$18432$ |
$1.161089$ |
$545338513/314721$ |
$1.16391$ |
$4.05069$ |
$[1, 1, 1, -4919, 4916]$ |
\(y^2+xy+y=x^3+x^2-4919x+4916\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 68.24.0-68.a.1.2, 132.24.0.?, 2244.48.0.? |
$[(-63, 295)]$ |
| 9537.b3 |
9537c1 |
9537.b |
9537c |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( 3 \cdot 11 \cdot 17^{7} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$4488$ |
$48$ |
$0$ |
$5.661432055$ |
$1$ |
|
$5$ |
$9216$ |
$0.814516$ |
$192100033/561$ |
$0.89524$ |
$3.93682$ |
$[1, 1, 1, -3474, 77166]$ |
\(y^2+xy+y=x^3+x^2-3474x+77166\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 136.24.0.?, 264.24.0.?, 1122.6.0.?, $\ldots$ |
$[(291, 4734)]$ |
| 9537.b4 |
9537c4 |
9537.b |
9537c |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{4} \cdot 11^{4} \cdot 17^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$4488$ |
$48$ |
$0$ |
$1.415358013$ |
$1$ |
|
$4$ |
$36864$ |
$1.507664$ |
$34741712447/20160657$ |
$0.99882$ |
$4.50407$ |
$[1, 1, 1, 19646, 63872]$ |
\(y^2+xy+y=x^3+x^2+19646x+63872\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 68.24.0-68.h.1.1, 264.24.0.?, 4488.48.0.? |
$[(1, 288)]$ |
| 9537.c1 |
9537d1 |
9537.c |
9537d |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{11} \cdot 11^{2} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$4.114101929$ |
$1$ |
|
$2$ |
$12672$ |
$0.937190$ |
$-337930850201473/21434787$ |
$0.98519$ |
$4.26942$ |
$[1, 1, 1, -9594, -365718]$ |
\(y^2+xy+y=x^3+x^2-9594x-365718\) |
6.2.0.a.1 |
$[(146, 1098)]$ |
| 9537.d1 |
9537m1 |
9537.d |
9537m |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{11} \cdot 11^{2} \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$215424$ |
$2.353798$ |
$-337930850201473/21434787$ |
$0.98519$ |
$6.12464$ |
$[1, 0, 0, -2772672, -1777362957]$ |
\(y^2+xy=x^3-2772672x-1777362957\) |
6.2.0.a.1 |
$[]$ |
| 9537.e1 |
9537f1 |
9537.e |
9537f |
$2$ |
$3$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{6} \cdot 11^{3} \cdot 17^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1122$ |
$16$ |
$0$ |
$0.360405218$ |
$1$ |
|
$12$ |
$6048$ |
$0.584433$ |
$-2412468600832/970299$ |
$1.00247$ |
$3.73011$ |
$[0, -1, 1, -1847, 31187]$ |
\(y^2+y=x^3-x^2-1847x+31187\) |
3.4.0.a.1, 22.2.0.a.1, 51.8.0-3.a.1.2, 66.8.0.a.1, 1122.16.0.? |
$[(5, 148), (377/4, 859/4)]$ |
| 9537.e2 |
9537f2 |
9537.e |
9537f |
$2$ |
$3$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{2} \cdot 11^{9} \cdot 17^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1122$ |
$16$ |
$0$ |
$0.360405218$ |
$1$ |
|
$12$ |
$18144$ |
$1.133739$ |
$682417553408/21221529219$ |
$1.07337$ |
$4.02498$ |
$[0, -1, 1, 1213, 117632]$ |
\(y^2+y=x^3-x^2+1213x+117632\) |
3.4.0.a.1, 22.2.0.a.1, 51.8.0-3.a.1.1, 66.8.0.a.1, 1122.16.0.? |
$[(173/2, 3989/2), (376, 7320)]$ |
| 9537.f1 |
9537a1 |
9537.f |
9537a |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{4} \cdot 11 \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$0.840912406$ |
$1$ |
|
$4$ |
$1152$ |
$-0.270616$ |
$-557056/891$ |
$0.85072$ |
$2.20697$ |
$[0, -1, 1, -11, -25]$ |
\(y^2+y=x^3-x^2-11x-25\) |
22.2.0.a.1 |
$[(5, 4)]$ |
| 9537.g1 |
9537g1 |
9537.g |
9537g |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{4} \cdot 11 \cdot 17^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$0.287529433$ |
$1$ |
|
$4$ |
$2304$ |
$0.323066$ |
$-75759616/891$ |
$0.99852$ |
$3.21906$ |
$[0, -1, 1, -385, 3069]$ |
\(y^2+y=x^3-x^2-385x+3069\) |
22.2.0.a.1 |
$[(-11, 76)]$ |
| 9537.h1 |
9537b1 |
9537.h |
9537b |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{2} \cdot 11^{5} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$374$ |
$2$ |
$0$ |
$0.721278957$ |
$1$ |
|
$4$ |
$46080$ |
$1.648769$ |
$-2160697802752/24640803$ |
$1.02074$ |
$4.95695$ |
$[0, -1, 1, -77837, 8466434]$ |
\(y^2+y=x^3-x^2-77837x+8466434\) |
374.2.0.? |
$[(176, 433)]$ |
| 9537.i1 |
9537h1 |
9537.i |
9537h |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{4} \cdot 11 \cdot 17^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$39168$ |
$1.739672$ |
$-75759616/891$ |
$0.99852$ |
$5.07428$ |
$[0, 1, 1, -111361, 14411239]$ |
\(y^2+y=x^3+x^2-111361x+14411239\) |
22.2.0.a.1 |
$[]$ |
| 9537.j1 |
9537l1 |
9537.j |
9537l |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{4} \cdot 11 \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$19584$ |
$1.145990$ |
$-557056/891$ |
$0.85072$ |
$4.06219$ |
$[0, 1, 1, -3275, -141067]$ |
\(y^2+y=x^3+x^2-3275x-141067\) |
22.2.0.a.1 |
$[]$ |
| 9537.k1 |
9537i1 |
9537.k |
9537i |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{10} \cdot 11 \cdot 17^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$374$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$92160$ |
$2.021893$ |
$-5736108018368512/11042163$ |
$1.03559$ |
$5.81526$ |
$[0, 1, 1, -1077777, -431027062]$ |
\(y^2+y=x^3+x^2-1077777x-431027062\) |
374.2.0.? |
$[]$ |
| 9537.l1 |
9537k1 |
9537.l |
9537k |
$2$ |
$3$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{6} \cdot 11^{3} \cdot 17^{8} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$66$ |
$16$ |
$0$ |
$6.565156973$ |
$1$ |
|
$4$ |
$102816$ |
$2.001038$ |
$-2412468600832/970299$ |
$1.00247$ |
$5.58534$ |
$[0, 1, 1, -533879, 150019865]$ |
\(y^2+y=x^3+x^2-533879x+150019865\) |
3.8.0-3.a.1.2, 22.2.0.a.1, 66.16.0-66.a.1.4 |
$[(3175, 174559)]$ |
| 9537.l2 |
9537k2 |
9537.l |
9537k |
$2$ |
$3$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{2} \cdot 11^{9} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$66$ |
$16$ |
$0$ |
$19.69547092$ |
$1$ |
|
$0$ |
$308448$ |
$2.550346$ |
$682417553408/21221529219$ |
$1.07337$ |
$5.88020$ |
$[0, 1, 1, 350461, 580030190]$ |
\(y^2+y=x^3+x^2+350461x+580030190\) |
3.8.0-3.a.1.1, 22.2.0.a.1, 66.16.0-66.a.1.1 |
$[(299108901/310, 5315207019349/310)]$ |
| 9537.m1 |
9537j3 |
9537.m |
9537j |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( 3^{3} \cdot 11^{4} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$4488$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$30720$ |
$1.403975$ |
$347873904937/395307$ |
$1.00913$ |
$4.75551$ |
$[1, 0, 1, -42345, 3347029]$ |
\(y^2+xy+y=x^3-42345x+3347029\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 68.12.0-4.c.1.2, 88.12.0.?, $\ldots$ |
$[]$ |
| 9537.m2 |
9537j2 |
9537.m |
9537j |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( 3^{6} \cdot 11^{2} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$2244$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$15360$ |
$1.057402$ |
$169112377/88209$ |
$1.00669$ |
$3.92291$ |
$[1, 0, 1, -3330, 22951]$ |
\(y^2+xy+y=x^3-3330x+22951\) |
2.6.0.a.1, 12.12.0.a.1, 44.12.0.b.1, 68.12.0-2.a.1.1, 132.24.0.?, $\ldots$ |
$[]$ |
| 9537.m3 |
9537j1 |
9537.m |
9537j |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( 3^{3} \cdot 11 \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$4488$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$7680$ |
$0.710828$ |
$30664297/297$ |
$1.09706$ |
$3.73656$ |
$[1, 0, 1, -1885, -31381]$ |
\(y^2+xy+y=x^3-1885x-31381\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 66.6.0.a.1, 88.12.0.?, $\ldots$ |
$[]$ |
| 9537.m4 |
9537j4 |
9537.m |
9537j |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 17^{2} \) |
\( - 3^{12} \cdot 11 \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$4488$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$30720$ |
$1.403975$ |
$9090072503/5845851$ |
$1.03763$ |
$4.35774$ |
$[1, 0, 1, 12565, 181901]$ |
\(y^2+xy+y=x^3+12565x+181901\) |
2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 44.12.0.g.1, $\ldots$ |
$[]$ |
