| 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 |
| 258.a1 |
258b1 |
258.a |
258b |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 43 \) |
\( 2^{14} \cdot 3^{7} \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$1032$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$196$ |
$0.650807$ |
$778510269523657/1540767744$ |
$1.00479$ |
$6.17480$ |
$[1, 1, 0, -1916, 31440]$ |
\(y^2+xy=x^3+x^2-1916x+31440\) |
2.3.0.a.1, 8.6.0.d.1, 258.6.0.?, 1032.12.0.? |
$[]$ |
| 258.a2 |
258b2 |
258.a |
258b |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{7} \cdot 3^{14} \cdot 43^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$1032$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$392$ |
$0.997380$ |
$-230042158153417/1131994839168$ |
$1.03167$ |
$6.36074$ |
$[1, 1, 0, -1276, 53584]$ |
\(y^2+xy=x^3+x^2-1276x+53584\) |
2.3.0.a.1, 8.6.0.a.1, 516.6.0.?, 1032.12.0.? |
$[]$ |
| 258.b1 |
258a1 |
258.b |
258a |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{6} \cdot 3 \cdot 43 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$516$ |
$2$ |
$0$ |
$0.252328383$ |
$1$ |
|
$6$ |
$24$ |
$-0.566169$ |
$1685159/8256$ |
$0.89017$ |
$2.94396$ |
$[1, 1, 0, 3, -3]$ |
\(y^2+xy=x^3+x^2+3x-3\) |
516.2.0.? |
$[(2, 3)]$ |
| 258.c1 |
258c1 |
258.c |
258c |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{2} \cdot 3^{5} \cdot 43 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$516$ |
$2$ |
$0$ |
$0.033607720$ |
$1$ |
|
$16$ |
$40$ |
$-0.378676$ |
$-338608873/41796$ |
$0.90085$ |
$3.57173$ |
$[1, 0, 1, -15, 22]$ |
\(y^2+xy+y=x^3-15x+22\) |
516.2.0.? |
$[(5, 6)]$ |
| 258.d1 |
258d3 |
258.d |
258d |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 43 \) |
\( 2^{3} \cdot 3 \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.102 |
2B |
$1032$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$240$ |
$0.493077$ |
$18440127492397057/1032$ |
$1.01875$ |
$6.74475$ |
$[1, 1, 1, -5504, -159463]$ |
\(y^2+xy+y=x^3+x^2-5504x-159463\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 516.12.0.?, 1032.48.0.? |
$[]$ |
| 258.d2 |
258d2 |
258.d |
258d |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 43 \) |
\( 2^{6} \cdot 3^{2} \cdot 43^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.4 |
2Cs |
$1032$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$120$ |
$0.146503$ |
$4502751117697/1065024$ |
$1.04479$ |
$5.24688$ |
$[1, 1, 1, -344, -2599]$ |
\(y^2+xy+y=x^3+x^2-344x-2599\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 516.24.0.?, 1032.48.0.? |
$[]$ |
| 258.d3 |
258d4 |
258.d |
258d |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{3} \cdot 3^{4} \cdot 43^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.59 |
2B |
$1032$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$240$ |
$0.493077$ |
$-3107661785857/2215383048$ |
$0.98806$ |
$5.32468$ |
$[1, 1, 1, -304, -3175]$ |
\(y^2+xy+y=x^3+x^2-304x-3175\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 1032.48.0.? |
$[]$ |
| 258.d4 |
258d1 |
258.d |
258d |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 43 \) |
\( 2^{12} \cdot 3 \cdot 43 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.53 |
2B |
$1032$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$60$ |
$-0.200071$ |
$1532808577/528384$ |
$0.93069$ |
$3.80885$ |
$[1, 1, 1, -24, -39]$ |
\(y^2+xy+y=x^3+x^2-24x-39\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 258.6.0.?, 516.24.0.?, $\ldots$ |
$[]$ |
| 258.e1 |
258e1 |
258.e |
258e |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{2} \cdot 3^{19} \cdot 43 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$516$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$760$ |
$1.286427$ |
$-9500554530751882177/199908972324$ |
$1.04122$ |
$7.86930$ |
$[1, 1, 1, -44124, 3549153]$ |
\(y^2+xy+y=x^3+x^2-44124x+3549153\) |
516.2.0.? |
$[]$ |
| 258.f1 |
258f2 |
258.f |
258f |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{2} \cdot 3 \cdot 43^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.5 |
7B.1.3 |
$3612$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$1176$ |
$1.418922$ |
$-23769846831649063249/3261823333284$ |
$1.04406$ |
$8.03449$ |
$[1, 0, 0, -59901, -5648523]$ |
\(y^2+xy=x^3-59901x-5648523\) |
7.48.0-7.a.2.2, 516.2.0.?, 3612.96.2.? |
$[]$ |
| 258.f2 |
258f1 |
258.f |
258f |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{14} \cdot 3^{7} \cdot 43 \) |
$0$ |
$\Z/7\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.1 |
7B.1.1 |
$3612$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$6$ |
$168$ |
$0.445967$ |
$444369620591/1540767744$ |
$0.99664$ |
$5.11937$ |
$[1, 0, 0, 159, 1737]$ |
\(y^2+xy=x^3+159x+1737\) |
7.48.0-7.a.1.2, 516.2.0.?, 3612.96.2.? |
$[]$ |
| 258.g1 |
258g1 |
258.g |
258g |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 43 \) |
\( 2^{2} \cdot 3 \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$1032$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$12$ |
$-0.789496$ |
$912673/516$ |
$0.90862$ |
$2.47150$ |
$[1, 0, 0, -2, 0]$ |
\(y^2+xy=x^3-2x\) |
2.3.0.a.1, 8.6.0.d.1, 258.6.0.?, 1032.12.0.? |
$[]$ |
| 258.g2 |
258g2 |
258.g |
258g |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2 \cdot 3^{2} \cdot 43^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$1032$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$24$ |
$-0.442923$ |
$56181887/33282$ |
$0.96315$ |
$3.21344$ |
$[1, 0, 0, 8, 2]$ |
\(y^2+xy=x^3+8x+2\) |
2.3.0.a.1, 8.6.0.a.1, 516.6.0.?, 1032.12.0.? |
$[]$ |
