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 |
1620.a1 |
1620b2 |
1620.a |
1620b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1296$ |
$0.653074$ |
$221184/125$ |
$1.42657$ |
$4.19953$ |
$[0, 0, 0, -648, -972]$ |
\(y^2=x^3-648x-972\) |
3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1 |
$[]$ |
1620.a2 |
1620b1 |
1620.a |
1620b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$432$ |
$0.103768$ |
$362225664/5$ |
$1.03419$ |
$4.01173$ |
$[0, 0, 0, -408, 3172]$ |
\(y^2=x^3-408x+3172\) |
3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4 |
$[]$ |
1620.b1 |
1620f1 |
1620.b |
1620f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( - 2^{8} \cdot 3^{6} \cdot 5 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$60$ |
$16$ |
$0$ |
$0.959836509$ |
$1$ |
|
$10$ |
$216$ |
$-0.080477$ |
$-148176/5$ |
$0.76106$ |
$3.26104$ |
$[0, 0, 0, -63, 198]$ |
\(y^2=x^3-63x+198\) |
3.8.0-3.a.1.2, 20.2.0.a.1, 60.16.0-60.a.1.8 |
$[(6, 6)]$ |
1620.b2 |
1620f2 |
1620.b |
1620f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( - 2^{8} \cdot 3^{10} \cdot 5^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$60$ |
$16$ |
$0$ |
$2.879509529$ |
$1$ |
|
$2$ |
$648$ |
$0.468829$ |
$191664/125$ |
$0.87436$ |
$3.88283$ |
$[0, 0, 0, 297, 702]$ |
\(y^2=x^3+297x+702\) |
3.8.0-3.a.1.1, 20.2.0.a.1, 60.16.0-60.a.1.5 |
$[(-2, 10)]$ |
1620.c1 |
1620a2 |
1620.c |
1620a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3888$ |
$1.278324$ |
$4045602816/1953125$ |
$1.18271$ |
$5.23021$ |
$[0, 0, 0, -8208, 116532]$ |
\(y^2=x^3-8208x+116532\) |
3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1 |
$[]$ |
1620.c2 |
1620a1 |
1620.c |
1620a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$1296$ |
$0.729018$ |
$183711891456/125$ |
$1.15925$ |
$5.15190$ |
$[0, 0, 0, -6768, 214308]$ |
\(y^2=x^3-6768x+214308\) |
3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4 |
$[]$ |
1620.d1 |
1620e2 |
1620.d |
1620e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{10} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$1.515330705$ |
$1$ |
|
$2$ |
$1296$ |
$0.653074$ |
$362225664/5$ |
$1.03419$ |
$4.90368$ |
$[0, 0, 0, -3672, -85644]$ |
\(y^2=x^3-3672x-85644\) |
3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1 |
$[(-35, 1)]$ |
1620.d2 |
1620e1 |
1620.d |
1620e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$0.505110235$ |
$1$ |
|
$12$ |
$432$ |
$0.103768$ |
$221184/125$ |
$1.42657$ |
$3.30758$ |
$[0, 0, 0, -72, 36]$ |
\(y^2=x^3-72x+36\) |
3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4 |
$[(0, 6)]$ |
1620.e1 |
1620c2 |
1620.e |
1620c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( - 2^{8} \cdot 3^{12} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$60$ |
$16$ |
$0$ |
$5.925631091$ |
$1$ |
|
$0$ |
$648$ |
$0.468829$ |
$-148176/5$ |
$0.76106$ |
$4.15299$ |
$[0, 0, 0, -567, -5346]$ |
\(y^2=x^3-567x-5346\) |
3.8.0-3.a.1.1, 20.2.0.a.1, 60.16.0-60.a.1.5 |
$[(250/3, 496/3)]$ |
1620.e2 |
1620c1 |
1620.e |
1620c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( - 2^{8} \cdot 3^{4} \cdot 5^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$60$ |
$16$ |
$0$ |
$1.975210363$ |
$1$ |
|
$6$ |
$216$ |
$-0.080477$ |
$191664/125$ |
$0.87436$ |
$2.99088$ |
$[0, 0, 0, 33, -26]$ |
\(y^2=x^3+33x-26\) |
3.8.0-3.a.1.2, 20.2.0.a.1, 60.16.0-60.a.1.8 |
$[(15, 62)]$ |
1620.f1 |
1620d2 |
1620.f |
1620d |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$3.291453281$ |
$1$ |
|
$0$ |
$3888$ |
$1.278324$ |
$183711891456/125$ |
$1.15925$ |
$6.04385$ |
$[0, 0, 0, -60912, -5786316]$ |
\(y^2=x^3-60912x-5786316\) |
3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1 |
$[(-1283/3, 35/3)]$ |
1620.f2 |
1620d1 |
1620.f |
1620d |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{9} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1.097151093$ |
$1$ |
|
$6$ |
$1296$ |
$0.729018$ |
$4045602816/1953125$ |
$1.18271$ |
$4.33826$ |
$[0, 0, 0, -912, -4316]$ |
\(y^2=x^3-912x-4316\) |
3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4 |
$[(-27, 25)]$ |