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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
142.a1 |
142b1 |
142.a |
142b |
$1$ |
$1$ |
\( 2 \cdot 71 \) |
\( 2 \cdot 71 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$568$ |
$2$ |
$0$ |
$0.180913710$ |
$1$ |
|
$6$ |
$4$ |
$-0.886641$ |
$389017/142$ |
$[1, 1, 0, -1, -1]$ |
\(y^2+xy=x^3+x^2-x-1\) |
568.2.0.? |
$[(-1, 1)]$ |
142.b1 |
142c2 |
142.b |
142c |
$2$ |
$2$ |
\( 2 \cdot 71 \) |
\( 2^{3} \cdot 71^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$568$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$18$ |
$-0.270967$ |
$7727161833/40328$ |
$[1, -1, 0, -41, -91]$ |
\(y^2+xy=x^3-x^2-41x-91\) |
2.3.0.a.1, 8.6.0.b.1, 284.6.0.?, 568.12.0.? |
$[]$ |
142.b2 |
142c1 |
142.b |
142c |
$2$ |
$2$ |
\( 2 \cdot 71 \) |
\( - 2^{6} \cdot 71 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$568$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$9$ |
$-0.617540$ |
$-185193/4544$ |
$[1, -1, 0, -1, -3]$ |
\(y^2+xy=x^3-x^2-x-3\) |
2.3.0.a.1, 8.6.0.c.1, 142.6.0.?, 568.12.0.? |
$[]$ |
142.c1 |
142e1 |
142.c |
142e |
$1$ |
$1$ |
\( 2 \cdot 71 \) |
\( 2^{27} \cdot 71 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$568$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$324$ |
$0.764042$ |
$2003092024307193/9529458688$ |
$[1, -1, 0, -2626, 52244]$ |
\(y^2+xy=x^3-x^2-2626x+52244\) |
568.2.0.? |
$[]$ |
142.d1 |
142a1 |
142.d |
142a |
$1$ |
$1$ |
\( 2 \cdot 71 \) |
\( 2^{9} \cdot 71 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$568$ |
$2$ |
$0$ |
$0.033789142$ |
$1$ |
|
$14$ |
$36$ |
$-0.409599$ |
$176558481/36352$ |
$[1, -1, 1, -12, 15]$ |
\(y^2+xy+y=x^3-x^2-12x+15\) |
568.2.0.? |
$[(1, 1)]$ |
142.e1 |
142d2 |
142.e |
142d |
$2$ |
$3$ |
\( 2 \cdot 71 \) |
\( 2 \cdot 71^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$1704$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12$ |
$-0.103537$ |
$21601086625/715822$ |
$[1, 0, 0, -58, -170]$ |
\(y^2+xy=x^3-58x-170\) |
3.8.0-3.a.1.1, 568.2.0.?, 1704.16.0.? |
$[]$ |
142.e2 |
142d1 |
142.e |
142d |
$2$ |
$3$ |
\( 2 \cdot 71 \) |
\( 2^{3} \cdot 71 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1704$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$4$ |
$-0.652843$ |
$57066625/568$ |
$[1, 0, 0, -8, 8]$ |
\(y^2+xy=x^3-8x+8\) |
3.8.0-3.a.1.2, 568.2.0.?, 1704.16.0.? |
$[]$ |