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 |
240.a1 |
240c4 |
240.a |
240c |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{11} \cdot 3^{4} \cdot 5 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$120$ |
$48$ |
$0$ |
$0.222905284$ |
$1$ |
|
$11$ |
$64$ |
$0.069403$ |
$546718898/405$ |
$0.99169$ |
$5.06220$ |
$[0, -1, 0, -216, 1296]$ |
\(y^2=x^3-x^2-216x+1296\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.2, 24.24.0-24.y.1.16, $\ldots$ |
$[(8, 4)]$ |
240.a2 |
240c3 |
240.a |
240c |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{11} \cdot 3 \cdot 5^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$120$ |
$48$ |
$0$ |
$0.891621139$ |
$1$ |
|
$7$ |
$64$ |
$0.069403$ |
$136835858/1875$ |
$0.97925$ |
$4.80946$ |
$[0, -1, 0, -136, -560]$ |
\(y^2=x^3-x^2-136x-560\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.2, 24.24.0-24.s.1.3, $\ldots$ |
$[(-6, 2)]$ |
240.a3 |
240c2 |
240.a |
240c |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$120$ |
$48$ |
$0$ |
$0.445810569$ |
$1$ |
|
$17$ |
$32$ |
$-0.277171$ |
$470596/225$ |
$1.13245$ |
$3.64797$ |
$[0, -1, 0, -16, 16]$ |
\(y^2=x^3-x^2-16x+16\) |
2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 24.24.0-24.b.1.3, $\ldots$ |
$[(0, 4)]$ |
240.a4 |
240c1 |
240.a |
240c |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{8} \cdot 3 \cdot 5 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$120$ |
$48$ |
$0$ |
$0.891621139$ |
$1$ |
|
$5$ |
$16$ |
$-0.623744$ |
$21296/15$ |
$0.85611$ |
$2.83023$ |
$[0, -1, 0, 4, 0]$ |
\(y^2=x^3-x^2+4x\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.1, 20.12.0-4.c.1.1, $\ldots$ |
$[(1, 2)]$ |
240.b1 |
240b8 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{15} \cdot 3^{4} \cdot 5^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.8, 3.4.0.1 |
2B, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$1.257313$ |
$16778985534208729/81000$ |
$1.08181$ |
$8.33419$ |
$[0, -1, 0, -85336, 9623536]$ |
\(y^2=x^3-x^2-85336x+9623536\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.4, $\ldots$ |
$[]$ |
240.b2 |
240b7 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{15} \cdot 3 \cdot 5^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.7, 3.4.0.1 |
2B, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$1.257313$ |
$10316097499609/5859375000$ |
$1.13600$ |
$6.98504$ |
$[0, -1, 0, -7256, 34800]$ |
\(y^2=x^3-x^2-7256x+34800\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.3, $\ldots$ |
$[]$ |
240.b3 |
240b6 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{18} \cdot 3^{2} \cdot 5^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.1, 3.4.0.1 |
2Cs, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$3$ |
$288$ |
$0.910740$ |
$4102915888729/9000000$ |
$1.05221$ |
$6.81681$ |
$[0, -1, 0, -5336, 151536]$ |
\(y^2=x^3-x^2-5336x+151536\) |
2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 8.12.0-2.a.1.1, 12.96.0-12.a.1.3, $\ldots$ |
$[]$ |
240.b4 |
240b4 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{13} \cdot 3^{3} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.7, 3.4.0.1 |
2B, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.708007$ |
$2656166199049/33750$ |
$1.05017$ |
$6.73748$ |
$[0, -1, 0, -4616, -119184]$ |
\(y^2=x^3-x^2-4616x-119184\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.3, $\ldots$ |
$[]$ |
240.b5 |
240b5 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{13} \cdot 3^{12} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.8, 3.4.0.1 |
2B, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.708007$ |
$35578826569/5314410$ |
$1.03393$ |
$5.95054$ |
$[0, -1, 0, -1096, 12400]$ |
\(y^2=x^3-x^2-1096x+12400\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.4, $\ldots$ |
$[]$ |
240.b6 |
240b2 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.1, 3.4.0.1 |
2Cs, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$3$ |
$96$ |
$0.361434$ |
$702595369/72900$ |
$1.00457$ |
$5.23444$ |
$[0, -1, 0, -296, -1680]$ |
\(y^2=x^3-x^2-296x-1680\) |
2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 8.12.0-2.a.1.1, 12.96.0-12.a.2.7, $\ldots$ |
$[]$ |
240.b7 |
240b3 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{24} \cdot 3 \cdot 5^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.12, 3.4.0.1 |
2B, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$144$ |
$0.564166$ |
$-273359449/1536000$ |
$1.04920$ |
$5.49483$ |
$[0, -1, 0, -216, 4080]$ |
\(y^2=x^3-x^2-216x+4080\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.2, $\ldots$ |
$[]$ |
240.b8 |
240b1 |
240.b |
240b |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3^{3} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.12, 3.4.0.1 |
2B, 3B |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$0.014860$ |
$357911/2160$ |
$0.99689$ |
$4.26037$ |
$[0, -1, 0, 24, -144]$ |
\(y^2=x^3-x^2+24x-144\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.2, $\ldots$ |
$[]$ |
240.c1 |
240a5 |
240.c |
240a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{11} \cdot 3 \cdot 5^{2} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.31 |
2B |
$240$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$128$ |
$0.479999$ |
$1770025017602/75$ |
$1.12837$ |
$6.53694$ |
$[0, -1, 0, -3200, 70752]$ |
\(y^2=x^3-x^2-3200x+70752\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.f.1.4, 24.48.0-24.bj.1.5, $\ldots$ |
$[]$ |
240.c2 |
240a3 |
240.c |
240a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.27 |
2Cs |
$120$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$7$ |
$64$ |
$0.133425$ |
$868327204/5625$ |
$1.10029$ |
$5.02014$ |
$[0, -1, 0, -200, 1152]$ |
\(y^2=x^3-x^2-200x+1152\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.1.10, 24.96.0-24.k.1.2, 40.96.0-40.v.1.7, $\ldots$ |
$[]$ |
240.c3 |
240a6 |
240.c |
240a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{11} \cdot 3 \cdot 5^{8} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.162 |
2B |
$240$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$128$ |
$0.479999$ |
$-27995042/1171875$ |
$1.07729$ |
$5.30361$ |
$[0, -1, 0, -80, 2400]$ |
\(y^2=x^3-x^2-80x+2400\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.1.2, 24.96.0-24.bo.1.4, 80.96.0.?, $\ldots$ |
$[]$ |
240.c4 |
240a2 |
240.c |
240a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.33 |
2Cs |
$120$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$32$ |
$-0.213148$ |
$3631696/2025$ |
$1.02576$ |
$3.76788$ |
$[0, -1, 0, -20, 0]$ |
\(y^2=x^3-x^2-20x\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.2.2, 20.48.0-20.c.1.2, 24.96.0-24.p.2.4, $\ldots$ |
$[]$ |
240.c5 |
240a1 |
240.c |
240a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.47 |
2B |
$240$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.559722$ |
$24918016/45$ |
$0.99237$ |
$3.61339$ |
$[0, -1, 0, -15, -18]$ |
\(y^2=x^3-x^2-15x-18\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 10.6.0.a.1, 16.48.0-16.f.2.11, $\ldots$ |
$[]$ |
240.c6 |
240a4 |
240.c |
240a |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{10} \cdot 3^{8} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.178 |
2B |
$240$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$64$ |
$0.133425$ |
$54607676/32805$ |
$1.06524$ |
$4.51538$ |
$[0, -1, 0, 80, -80]$ |
\(y^2=x^3-x^2+80x-80\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 20.24.0-20.h.1.1, 40.96.0-40.bm.2.4, $\ldots$ |
$[]$ |
240.d1 |
240d7 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.104 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$256$ |
$0.984016$ |
$1114544804970241/405$ |
$1.07354$ |
$7.83941$ |
$[0, 1, 0, -34560, 2461428]$ |
\(y^2=x^3+x^2-34560x+2461428\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 10.6.0.a.1, 16.96.0-16.x.2.3, $\ldots$ |
$[]$ |
240.d2 |
240d5 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.41 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$7$ |
$128$ |
$0.637444$ |
$272223782641/164025$ |
$1.03897$ |
$6.32183$ |
$[0, 1, 0, -2160, 37908]$ |
\(y^2=x^3+x^2-2160x+37908\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.k.1.2, 20.48.0-20.c.1.1, 40.192.1-40.cc.2.1, $\ldots$ |
$[]$ |
240.d3 |
240d8 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3^{16} \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.101 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$256$ |
$0.984016$ |
$-147281603041/215233605$ |
$1.05949$ |
$6.43964$ |
$[0, 1, 0, -1760, 52788]$ |
\(y^2=x^3+x^2-1760x+52788\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.2.2, 16.96.0-16.u.2.4, 20.24.0-20.h.1.2, $\ldots$ |
$[]$ |
240.d4 |
240d3 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3 \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.96.0.13 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$4$ |
$2$ |
$1$ |
$64$ |
$0.290870$ |
$56667352321/15$ |
$1.03019$ |
$6.03547$ |
$[0, 1, 0, -1280, -18060]$ |
\(y^2=x^3+x^2-1280x-18060\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 24.48.0-24.by.2.11, $\ldots$ |
$[]$ |
240.d5 |
240d4 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.1 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$7$ |
$64$ |
$0.290870$ |
$111284641/50625$ |
$1.02534$ |
$4.89822$ |
$[0, 1, 0, -160, 308]$ |
\(y^2=x^3+x^2-160x+308\) |
2.6.0.a.1, 4.48.0-4.b.1.1, 8.96.0-8.b.2.2, 24.192.1-24.n.1.6, 40.192.1-40.s.1.2, $\ldots$ |
$[]$ |
240.d6 |
240d2 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.9 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$32$ |
$-0.055704$ |
$13997521/225$ |
$0.96230$ |
$4.51994$ |
$[0, 1, 0, -80, -300]$ |
\(y^2=x^3+x^2-80x-300\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.i.1.2, 16.96.0-16.d.2.2, 24.96.0-24.bb.2.1, $\ldots$ |
$[]$ |
240.d7 |
240d1 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3 \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.96.0.13 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.402277$ |
$-1/15$ |
$1.19808$ |
$3.37197$ |
$[0, 1, 0, 0, -12]$ |
\(y^2=x^3+x^2-12\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 24.48.0-24.bz.1.11, $\ldots$ |
$[]$ |
240.d8 |
240d6 |
240.d |
240d |
$8$ |
$16$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3^{2} \cdot 5^{8} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.101 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$128$ |
$0.637444$ |
$4733169839/3515625$ |
$1.05585$ |
$5.58249$ |
$[0, 1, 0, 560, 2900]$ |
\(y^2=x^3+x^2+560x+2900\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 8.96.0-8.n.2.2, 24.192.1-24.cv.2.5, 80.192.1.?, $\ldots$ |
$[]$ |