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 |
405.a1 |
405f1 |
405.a |
405f |
$1$ |
$1$ |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$10$ |
$2$ |
$0$ |
$0.272277013$ |
$1$ |
|
$6$ |
$24$ |
$-0.772497$ |
$36864/5$ |
$0.77778$ |
$2.48330$ |
$[0, 0, 1, -3, -2]$ |
\(y^2+y=x^3-3x-2\) |
10.2.0.a.1 |
$[(-1, 0)]$ |
405.b1 |
405d2 |
405.b |
405d |
$2$ |
$7$ |
\( 3^{4} \cdot 5 \) |
\( - 3^{10} \cdot 5^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.8.0.1 |
7B |
$1260$ |
$96$ |
$2$ |
$0.043718464$ |
$1$ |
|
$12$ |
$252$ |
$0.701672$ |
$-15590912409/78125$ |
$1.00703$ |
$5.74040$ |
$[1, -1, 1, -2027, 35776]$ |
\(y^2+xy+y=x^3-x^2-2027x+35776\) |
7.8.0.a.1, 20.2.0.a.1, 21.16.0-7.a.1.1, 63.48.0-63.b.1.3, 140.16.0.?, $\ldots$ |
$[(76, 524)]$ |
405.b2 |
405d1 |
405.b |
405d |
$2$ |
$7$ |
\( 3^{4} \cdot 5 \) |
\( - 3^{10} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.8.0.1 |
7B |
$1260$ |
$96$ |
$2$ |
$0.306029253$ |
$1$ |
|
$8$ |
$36$ |
$-0.271284$ |
$-9/5$ |
$1.00480$ |
$3.33972$ |
$[1, -1, 1, -2, -26]$ |
\(y^2+xy+y=x^3-x^2-2x-26\) |
7.8.0.a.1, 20.2.0.a.1, 21.16.0-7.a.1.2, 63.48.0-63.b.2.2, 140.16.0.?, $\ldots$ |
$[(4, 2)]$ |
405.c1 |
405b2 |
405.c |
405b |
$2$ |
$3$ |
\( 3^{4} \cdot 5 \) |
\( 3^{10} \cdot 5^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$0.355512380$ |
$1$ |
|
$6$ |
$72$ |
$0.074670$ |
$2359296/125$ |
$1.10725$ |
$4.27390$ |
$[0, 0, 1, -108, -412]$ |
\(y^2+y=x^3-108x-412\) |
3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1 |
$[(-6, 4)]$ |
405.c2 |
405b1 |
405.c |
405b |
$2$ |
$3$ |
\( 3^{4} \cdot 5 \) |
\( 3^{6} \cdot 5 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1.066537142$ |
$1$ |
|
$6$ |
$24$ |
$-0.474636$ |
$884736/5$ |
$1.04562$ |
$3.37860$ |
$[0, 0, 1, -18, 29]$ |
\(y^2+y=x^3-18x+29\) |
3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4 |
$[(1, 3)]$ |
405.d1 |
405a2 |
405.d |
405a |
$2$ |
$3$ |
\( 3^{4} \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$72$ |
$0.074670$ |
$884736/5$ |
$1.04562$ |
$4.47650$ |
$[0, 0, 1, -162, -790]$ |
\(y^2+y=x^3-162x-790\) |
3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1 |
$[]$ |
405.d2 |
405a1 |
405.d |
405a |
$2$ |
$3$ |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$30$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$24$ |
$-0.474636$ |
$2359296/125$ |
$1.10725$ |
$3.17600$ |
$[0, 0, 1, -12, 15]$ |
\(y^2+y=x^3-12x+15\) |
3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4 |
$[]$ |
405.e1 |
405c2 |
405.e |
405c |
$2$ |
$7$ |
\( 3^{4} \cdot 5 \) |
\( - 3^{4} \cdot 5^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.16.0.2 |
7B.2.3 |
$1260$ |
$96$ |
$2$ |
$3.274202297$ |
$1$ |
|
$2$ |
$84$ |
$0.152365$ |
$-15590912409/78125$ |
$1.00703$ |
$4.64250$ |
$[1, -1, 0, -225, -1250]$ |
\(y^2+xy=x^3-x^2-225x-1250\) |
7.16.0-7.a.1.1, 20.2.0.a.1, 63.48.0-63.b.1.2, 140.32.0.?, 1260.96.2.? |
$[(18, 8)]$ |
405.e2 |
405c1 |
405.e |
405c |
$2$ |
$7$ |
\( 3^{4} \cdot 5 \) |
\( - 3^{4} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.16.0.1 |
7B.2.1 |
$1260$ |
$96$ |
$2$ |
$0.467743185$ |
$1$ |
|
$2$ |
$12$ |
$-0.820590$ |
$-9/5$ |
$1.00480$ |
$2.24182$ |
$[1, -1, 0, 0, 1]$ |
\(y^2+xy=x^3-x^2+1\) |
7.16.0-7.a.1.2, 20.2.0.a.1, 63.48.0-63.b.2.3, 140.32.0.?, 1260.96.2.? |
$[(0, 1)]$ |
405.f1 |
405e1 |
405.f |
405e |
$1$ |
$1$ |
\( 3^{4} \cdot 5 \) |
\( 3^{10} \cdot 5 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$10$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$72$ |
$-0.223191$ |
$36864/5$ |
$0.77778$ |
$3.58120$ |
$[0, 0, 1, -27, 47]$ |
\(y^2+y=x^3-27x+47\) |
10.2.0.a.1 |
$[]$ |