| 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 |
Manin constant |
| 4056.l1 |
4056q1 |
4056.l |
4056q |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$52$ |
$16$ |
$0$ |
$0.304833129$ |
$1$ |
|
$6$ |
$768$ |
$0.057616$ |
$69212/81$ |
$0.89849$ |
$2.79592$ |
$[0, 1, 0, 48, 144]$ |
\(y^2=x^3+x^2+48x+144\) |
4.8.0.b.1, 52.16.0-4.b.1.1 |
$[(0, 12)]$ |
$1$ |
| 4056.q1 |
4056g1 |
4056.q |
4056g |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.16.0.2 |
|
$4$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$9984$ |
$1.340090$ |
$69212/81$ |
$0.89849$ |
$4.64832$ |
$[0, 1, 0, 8056, 284064]$ |
\(y^2=x^3+x^2+8056x+284064\) |
4.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
| 8112.b1 |
8112d1 |
8112.b |
8112d |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$52$ |
$16$ |
$0$ |
$0.570319044$ |
$1$ |
|
$6$ |
$1536$ |
$0.057616$ |
$69212/81$ |
$0.89849$ |
$2.58061$ |
$[0, -1, 0, 48, -144]$ |
\(y^2=x^3-x^2+48x-144\) |
4.8.0.b.1, 52.16.0-4.b.1.1 |
$[(6, 18)]$ |
$1$ |
| 8112.n1 |
8112c1 |
8112.n |
8112c |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.16.0.2 |
|
$4$ |
$16$ |
$0$ |
$3.339875908$ |
$1$ |
|
$2$ |
$19968$ |
$1.340090$ |
$69212/81$ |
$0.89849$ |
$4.29037$ |
$[0, -1, 0, 8056, -284064]$ |
\(y^2=x^3-x^2+8056x-284064\) |
4.16.0-4.b.1.1 |
$[(110, 1386)]$ |
$1$ |
| 12168.d1 |
12168r1 |
12168.d |
12168r |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{10} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$12$ |
$16$ |
$0$ |
$4.675240145$ |
$1$ |
|
$2$ |
$79872$ |
$1.889397$ |
$69212/81$ |
$0.89849$ |
$4.80619$ |
$[0, 0, 0, 72501, -7597226]$ |
\(y^2=x^3+72501x-7597226\) |
4.8.0.b.1, 12.16.0-4.b.1.1 |
$[(755, 21852)]$ |
$1$ |
| 12168.u1 |
12168g1 |
12168.u |
12168g |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{10} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$156$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$6144$ |
$0.606922$ |
$69212/81$ |
$0.89849$ |
$3.17013$ |
$[0, 0, 0, 429, -3458]$ |
\(y^2=x^3+429x-3458\) |
4.8.0.b.1, 156.16.0.? |
$[ ]$ |
$1$ |
| 24336.i1 |
24336o1 |
24336.i |
24336o |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{10} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$12$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$159744$ |
$1.889397$ |
$69212/81$ |
$0.89849$ |
$4.47634$ |
$[0, 0, 0, 72501, 7597226]$ |
\(y^2=x^3+72501x+7597226\) |
4.8.0.b.1, 12.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
| 24336.cb1 |
24336m1 |
24336.cb |
24336m |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{10} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$156$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12288$ |
$0.606922$ |
$69212/81$ |
$0.89849$ |
$2.95256$ |
$[0, 0, 0, 429, 3458]$ |
\(y^2=x^3+429x+3458\) |
4.8.0.b.1, 156.16.0.? |
$[ ]$ |
$1$ |
| 32448.f1 |
32448j1 |
32448.f |
32448j |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{4} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.16.0.3 |
|
$8$ |
$16$ |
$0$ |
$0.482386668$ |
$1$ |
|
$6$ |
$159744$ |
$1.686665$ |
$69212/81$ |
$0.89849$ |
$4.11816$ |
$[0, -1, 0, 32223, 2240289]$ |
\(y^2=x^3-x^2+32223x+2240289\) |
4.8.0.b.1, 8.16.0-4.b.1.1 |
$[(113, 2704)]$ |
$1$ |
| 32448.bq1 |
32448h1 |
32448.bq |
32448h |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{4} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$104$ |
$16$ |
$0$ |
$0.710627852$ |
$1$ |
|
$4$ |
$12288$ |
$0.404190$ |
$69212/81$ |
$0.89849$ |
$2.63658$ |
$[0, -1, 0, 191, 961]$ |
\(y^2=x^3-x^2+191x+961\) |
4.8.0.b.1, 104.16.0.? |
$[(25, 144)]$ |
$1$ |
| 32448.cb1 |
32448de1 |
32448.cb |
32448de |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{4} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.16.0.3 |
|
$8$ |
$16$ |
$0$ |
$0.903532528$ |
$1$ |
|
$2$ |
$159744$ |
$1.686665$ |
$69212/81$ |
$0.89849$ |
$4.11816$ |
$[0, 1, 0, 32223, -2240289]$ |
\(y^2=x^3+x^2+32223x-2240289\) |
4.8.0.b.1, 8.16.0-4.b.1.1 |
$[(225, 4056)]$ |
$1$ |
| 32448.dk1 |
32448db1 |
32448.dk |
32448db |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{4} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$104$ |
$16$ |
$0$ |
$1.286283045$ |
$1$ |
|
$2$ |
$12288$ |
$0.404190$ |
$69212/81$ |
$0.89849$ |
$2.63658$ |
$[0, 1, 0, 191, -961]$ |
\(y^2=x^3+x^2+191x-961\) |
4.8.0.b.1, 104.16.0.? |
$[(5, 12)]$ |
$1$ |
| 97344.q1 |
97344cp1 |
97344.q |
97344cp |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{10} \cdot 13^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$312$ |
$16$ |
$0$ |
$2.507445461$ |
$1$ |
|
$14$ |
$98304$ |
$0.953496$ |
$69212/81$ |
$0.89849$ |
$2.95829$ |
$[0, 0, 0, 1716, -27664]$ |
\(y^2=x^3+1716x-27664\) |
4.8.0.b.1, 312.16.0.? |
$[(22, 144), (40, 324)]$ |
$1$ |
| 97344.r1 |
97344fw1 |
97344.r |
97344fw |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{10} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$312$ |
$16$ |
$0$ |
$2.132091015$ |
$1$ |
|
$2$ |
$98304$ |
$0.953496$ |
$69212/81$ |
$0.89849$ |
$2.95829$ |
$[0, 0, 0, 1716, 27664]$ |
\(y^2=x^3+1716x+27664\) |
4.8.0.b.1, 312.16.0.? |
$[(-4, 144)]$ |
$1$ |
| 97344.fy1 |
97344ck1 |
97344.fy |
97344ck |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{10} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$24$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1277952$ |
$2.235970$ |
$69212/81$ |
$0.89849$ |
$4.29815$ |
$[0, 0, 0, 290004, -60777808]$ |
\(y^2=x^3+290004x-60777808\) |
4.8.0.b.1, 24.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
| 97344.fz1 |
97344fp1 |
97344.fz |
97344fp |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{16} \cdot 3^{10} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$24$ |
$16$ |
$0$ |
$4.474402610$ |
$1$ |
|
$0$ |
$1277952$ |
$2.235970$ |
$69212/81$ |
$0.89849$ |
$4.29815$ |
$[0, 0, 0, 290004, 60777808]$ |
\(y^2=x^3+290004x+60777808\) |
4.8.0.b.1, 24.16.0-4.b.1.1 |
$[(-2704/5, 663156/5)]$ |
$1$ |
| 101400.y1 |
101400a1 |
101400.y |
101400a |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$260$ |
$16$ |
$0$ |
$1.897114620$ |
$1$ |
|
$2$ |
$82944$ |
$0.862335$ |
$69212/81$ |
$0.89849$ |
$2.85291$ |
$[0, -1, 0, 1192, 15612]$ |
\(y^2=x^3-x^2+1192x+15612\) |
4.8.0.b.1, 260.16.0.? |
$[(26, 252)]$ |
$1$ |
| 101400.z1 |
101400bz1 |
101400.z |
101400bz |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$20$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1078272$ |
$2.144810$ |
$69212/81$ |
$0.89849$ |
$4.18803$ |
$[0, -1, 0, 201392, 35105212]$ |
\(y^2=x^3-x^2+201392x+35105212\) |
4.8.0.b.1, 20.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
| 198744.e1 |
198744dh1 |
198744.e |
198744dh |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 7^{6} \cdot 13^{8} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$28$ |
$16$ |
$0$ |
$3.264972091$ |
$1$ |
|
$8$ |
$3833856$ |
$2.313046$ |
$69212/81$ |
$0.89849$ |
$4.12250$ |
$[0, -1, 0, 394728, -96644484]$ |
\(y^2=x^3-x^2+394728x-96644484\) |
4.8.0.b.1, 28.16.0-4.b.1.1 |
$[(282, 6084), (13802, 1623076)]$ |
$1$ |
| 198744.bo1 |
198744cb1 |
198744.bo |
198744cb |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 7^{6} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$364$ |
$16$ |
$0$ |
$2.495963079$ |
$1$ |
|
$2$ |
$294912$ |
$1.030571$ |
$69212/81$ |
$0.89849$ |
$2.86102$ |
$[0, -1, 0, 2336, -44708]$ |
\(y^2=x^3-x^2+2336x-44708\) |
4.8.0.b.1, 364.16.0.? |
$[(229, 3528)]$ |
$1$ |
| 202800.hv1 |
202800hy1 |
202800.hv |
202800hy |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$20$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2156544$ |
$2.144810$ |
$69212/81$ |
$0.89849$ |
$3.95047$ |
$[0, 1, 0, 201392, -35105212]$ |
\(y^2=x^3+x^2+201392x-35105212\) |
4.8.0.b.1, 20.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
| 202800.hw1 |
202800hz1 |
202800.hw |
202800hz |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$260$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$165888$ |
$0.862335$ |
$69212/81$ |
$0.89849$ |
$2.69108$ |
$[0, 1, 0, 1192, -15612]$ |
\(y^2=x^3+x^2+1192x-15612\) |
4.8.0.b.1, 260.16.0.? |
$[ ]$ |
$1$ |
| 304200.cz1 |
304200cz1 |
304200.cz |
304200cz |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{10} \cdot 5^{6} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$780$ |
$16$ |
$0$ |
$6.058611584$ |
$1$ |
|
$0$ |
$663552$ |
$1.411640$ |
$69212/81$ |
$0.89849$ |
$3.12676$ |
$[0, 0, 0, 10725, -432250]$ |
\(y^2=x^3+10725x-432250\) |
4.8.0.b.1, 780.16.0.? |
$[(1699/5, 97668/5)]$ |
$1$ |
| 304200.da1 |
304200da1 |
304200.da |
304200da |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{10} \cdot 5^{6} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$60$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$8626176$ |
$2.694115$ |
$69212/81$ |
$0.89849$ |
$4.34570$ |
$[0, 0, 0, 1812525, -949653250]$ |
\(y^2=x^3+1812525x-949653250\) |
4.8.0.b.1, 60.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
| 397488.fx1 |
397488fx1 |
397488.fx |
397488fx |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 7^{6} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$28$ |
$16$ |
$0$ |
$0.895622171$ |
$1$ |
|
$4$ |
$7667712$ |
$2.313046$ |
$69212/81$ |
$0.89849$ |
$3.90086$ |
$[0, 1, 0, 394728, 96644484]$ |
\(y^2=x^3+x^2+394728x+96644484\) |
4.8.0.b.1, 28.16.0-4.b.1.1 |
$[(2760, 149058)]$ |
$1$ |
| 397488.jq1 |
397488jq1 |
397488.jq |
397488jq |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 7^{6} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$364$ |
$16$ |
$0$ |
$1.569328689$ |
$1$ |
|
$2$ |
$589824$ |
$1.030571$ |
$69212/81$ |
$0.89849$ |
$2.70721$ |
$[0, 1, 0, 2336, 44708]$ |
\(y^2=x^3+x^2+2336x+44708\) |
4.8.0.b.1, 364.16.0.? |
$[(16, 294)]$ |
$1$ |
| 490776.bw1 |
490776bw1 |
490776.bw |
490776bw |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 11^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 11^{6} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$572$ |
$16$ |
$0$ |
$1.177240673$ |
$1$ |
|
$4$ |
$1105920$ |
$1.256563$ |
$69212/81$ |
$0.89849$ |
$2.87061$ |
$[0, 1, 0, 5768, -168544]$ |
\(y^2=x^3+x^2+5768x-168544\) |
4.8.0.b.1, 572.16.0.? |
$[(260, 4356)]$ |
$1$ |
| 490776.cw1 |
490776cw1 |
490776.cw |
490776cw |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 11^{2} \cdot 13^{2} \) |
\( - 2^{10} \cdot 3^{4} \cdot 11^{6} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$44$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$14376960$ |
$2.539040$ |
$69212/81$ |
$0.89849$ |
$4.04506$ |
$[0, 1, 0, 974736, -374190192]$ |
\(y^2=x^3+x^2+974736x-374190192\) |
4.8.0.b.1, 44.16.0-4.b.1.1 |
$[ ]$ |
$1$ |
