| 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 |
| 27380.a1 |
27380b1 |
27380.a |
27380b |
$1$ |
$1$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 37^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$74$ |
$2$ |
$0$ |
$2.236886492$ |
$1$ |
|
$0$ |
$703296$ |
$2.243320$ |
$1769472/25$ |
$0.98850$ |
$5.13132$ |
$[0, 0, 0, -810448, 277375828]$ |
\(y^2=x^3-810448x+277375828\) |
74.2.0.? |
$[(1369/2, 50653/2)]$ |
| 27380.b1 |
27380f1 |
27380.b |
27380f |
$1$ |
$1$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 37^{3} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$74$ |
$2$ |
$0$ |
$0.258071687$ |
$1$ |
|
$20$ |
$19008$ |
$0.437862$ |
$1769472/25$ |
$0.98850$ |
$3.01090$ |
$[0, 0, 0, -592, 5476]$ |
\(y^2=x^3-592x+5476\) |
74.2.0.? |
$[(0, 74), (12, 10)]$ |
| 27380.c1 |
27380d3 |
27380.c |
27380d |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{4} \cdot 5^{3} \cdot 37^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.3, 3.4.0.1 |
2B, 3B |
$4440$ |
$384$ |
$9$ |
$3.150035961$ |
$1$ |
|
$5$ |
$77760$ |
$1.424814$ |
$488095744/125$ |
$1.07376$ |
$4.34977$ |
$[0, 1, 0, -56585, -5198600]$ |
\(y^2=x^3+x^2-56585x-5198600\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 10.6.0.a.1, $\ldots$ |
$[(-137, 31)]$ |
| 27380.c2 |
27380d4 |
27380.c |
27380d |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( - 2^{8} \cdot 5^{6} \cdot 37^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.5, 3.4.0.1 |
2B, 3B |
$4440$ |
$384$ |
$9$ |
$1.575017980$ |
$1$ |
|
$7$ |
$155520$ |
$1.771389$ |
$-20720464/15625$ |
$0.95894$ |
$4.39357$ |
$[0, 1, 0, -49740, -6496412]$ |
\(y^2=x^3+x^2-49740x-6496412\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.24.0.d.1, $\ldots$ |
$[(308, 2738)]$ |
| 27380.c3 |
27380d1 |
27380.c |
27380d |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{4} \cdot 5 \cdot 37^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.3, 3.4.0.1 |
2B, 3B |
$4440$ |
$384$ |
$9$ |
$9.450107883$ |
$1$ |
|
$1$ |
$25920$ |
$0.875509$ |
$16384/5$ |
$0.95621$ |
$3.34151$ |
$[0, 1, 0, -1825, 20028]$ |
\(y^2=x^3+x^2-1825x+20028\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 10.6.0.a.1, $\ldots$ |
$[(332/17, 657944/17)]$ |
| 27380.c4 |
27380d2 |
27380.c |
27380d |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( - 2^{8} \cdot 5^{2} \cdot 37^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.5, 3.4.0.1 |
2B, 3B |
$4440$ |
$384$ |
$9$ |
$4.725053941$ |
$1$ |
|
$1$ |
$51840$ |
$1.222082$ |
$21296/25$ |
$0.83964$ |
$3.64129$ |
$[0, 1, 0, 5020, 140500]$ |
\(y^2=x^3+x^2+5020x+140500\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.24.0.d.1, $\ldots$ |
$[(8665/4, 814555/4)]$ |
| 27380.d1 |
27380a1 |
27380.d |
27380a |
$1$ |
$1$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{4} \cdot 37^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$74$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$131328$ |
$1.794575$ |
$40247296/23125$ |
$0.95030$ |
$4.37690$ |
$[0, -1, 0, -62061, 523465]$ |
\(y^2=x^3-x^2-62061x+523465\) |
74.2.0.? |
$[]$ |
| 27380.e1 |
27380c2 |
27380.e |
27380c |
$2$ |
$3$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 37^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$222$ |
$16$ |
$0$ |
$1.208388418$ |
$1$ |
|
$4$ |
$590976$ |
$2.681046$ |
$750484394082304/578125$ |
$1.10880$ |
$6.01537$ |
$[0, 1, 0, -16457205, -25702458025]$ |
\(y^2=x^3+x^2-16457205x-25702458025\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 74.2.0.?, 111.8.0.?, 222.16.0.? |
$[(6265, 342250)]$ |
| 27380.e2 |
27380c1 |
27380.e |
27380c |
$2$ |
$3$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 37^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$222$ |
$16$ |
$0$ |
$3.625165256$ |
$1$ |
|
$0$ |
$196992$ |
$2.131741$ |
$2575826944/1266325$ |
$0.99189$ |
$4.78393$ |
$[0, 1, 0, -248245, -18550457]$ |
\(y^2=x^3+x^2-248245x-18550457\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 74.2.0.?, 111.8.0.?, 222.16.0.? |
$[(34554/7, 4305505/7)]$ |
| 27380.f1 |
27380e1 |
27380.f |
27380e |
$1$ |
$1$ |
\( 2^{2} \cdot 5 \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 37^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$74$ |
$2$ |
$0$ |
$8.874866480$ |
$1$ |
|
$0$ |
$17072640$ |
$3.684959$ |
$4565397831743545344/27087483203125$ |
$1.06530$ |
$6.86814$ |
$[0, 0, 0, -300424312, 1993943796116]$ |
\(y^2=x^3-300424312x+1993943796116\) |
74.2.0.? |
$[(-8507/3, 40742875/3)]$ |
