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 |
270.a1 |
270a1 |
270.a |
270a |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2 \cdot 3^{9} \cdot 5 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$36$ |
$-0.279375$ |
$-19683/10$ |
$1.02991$ |
$3.64481$ |
$[1, -1, 0, -15, 35]$ |
\(y^2+xy=x^3-x^2-15x+35\) |
3.8.0-3.a.1.2, 120.16.0.? |
$[]$ |
270.a2 |
270a2 |
270.a |
270a |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2^{3} \cdot 3^{11} \cdot 5^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$108$ |
$0.269931$ |
$1073733/1000$ |
$0.96044$ |
$4.63905$ |
$[1, -1, 0, 120, -424]$ |
\(y^2+xy=x^3-x^2+120x-424\) |
3.8.0-3.a.1.1, 120.16.0.? |
$[]$ |
270.b1 |
270d1 |
270.b |
270d |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2^{5} \cdot 3^{3} \cdot 5^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$60$ |
$-0.045373$ |
$-16522921323/4000$ |
$1.05582$ |
$4.79140$ |
$[1, -1, 0, -159, 813]$ |
\(y^2+xy=x^3-x^2-159x+813\) |
3.8.0-3.a.1.2, 120.16.0.? |
$[]$ |
270.b2 |
270d2 |
270.b |
270d |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2^{15} \cdot 3^{9} \cdot 5 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$180$ |
$0.503934$ |
$1601613/163840$ |
$1.15089$ |
$5.24133$ |
$[1, -1, 0, 66, 2708]$ |
\(y^2+xy=x^3-x^2+66x+2708\) |
3.8.0-3.a.1.1, 120.16.0.? |
$[]$ |
270.c1 |
270b2 |
270.c |
270b |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2^{5} \cdot 3^{9} \cdot 5^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$180$ |
$0.503934$ |
$-16522921323/4000$ |
$1.05582$ |
$5.96881$ |
$[1, -1, 1, -1433, -20519]$ |
\(y^2+xy+y=x^3-x^2-1433x-20519\) |
3.8.0-3.a.1.1, 120.16.0.? |
$[]$ |
270.c2 |
270b1 |
270.c |
270b |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2^{15} \cdot 3^{3} \cdot 5 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$60$ |
$-0.045373$ |
$1601613/163840$ |
$1.15089$ |
$4.06392$ |
$[1, -1, 1, 7, -103]$ |
\(y^2+xy+y=x^3-x^2+7x-103\) |
3.8.0-3.a.1.2, 120.16.0.? |
$[]$ |
270.d1 |
270c1 |
270.d |
270c |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2 \cdot 3^{3} \cdot 5 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12$ |
$-0.828681$ |
$-19683/10$ |
$1.02991$ |
$2.46739$ |
$[1, -1, 1, -2, -1]$ |
\(y^2+xy+y=x^3-x^2-2x-1\) |
3.8.0-3.a.1.1, 120.16.0.? |
$[]$ |
270.d2 |
270c2 |
270.d |
270c |
$2$ |
$3$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
\( - 2^{3} \cdot 3^{5} \cdot 5^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$120$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$36$ |
$-0.279375$ |
$1073733/1000$ |
$0.96044$ |
$3.46164$ |
$[1, -1, 1, 13, 11]$ |
\(y^2+xy+y=x^3-x^2+13x+11\) |
3.8.0-3.a.1.2, 120.16.0.? |
$[]$ |