| 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 |
| 6069.a1 |
6069a1 |
6069.a |
6069a |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( - 3^{7} \cdot 7^{2} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$0.439005330$ |
$1$ |
|
$4$ |
$32256$ |
$1.338800$ |
$-8390176768/1821771$ |
$0.90870$ |
$4.61123$ |
$[0, -1, 1, -12234, 614882]$ |
\(y^2+y=x^3-x^2-12234x+614882\) |
102.2.0.? |
$[(125, 1011)]$ |
| 6069.b1 |
6069b5 |
6069.b |
6069b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( 3 \cdot 7^{2} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.13 |
2B |
$5712$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$0$ |
$18432$ |
$1.490812$ |
$53297461115137/147$ |
$1.05087$ |
$5.57990$ |
$[1, 1, 1, -226582, -41607616]$ |
\(y^2+xy+y=x^3+x^2-226582x-41607616\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$ |
$[]$ |
| 6069.b2 |
6069b3 |
6069.b |
6069b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.18 |
2Cs |
$2856$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$9216$ |
$1.144238$ |
$13027640977/21609$ |
$1.08149$ |
$4.62517$ |
$[1, 1, 1, -14167, -654004]$ |
\(y^2+xy+y=x^3+x^2-14167x-654004\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$ |
$[]$ |
| 6069.b3 |
6069b4 |
6069.b |
6069b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( 3^{8} \cdot 7 \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.88 |
2B |
$5712$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$9216$ |
$1.144238$ |
$6570725617/45927$ |
$1.00160$ |
$4.54660$ |
$[1, 1, 1, -11277, 453444]$ |
\(y^2+xy+y=x^3+x^2-11277x+453444\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$ |
$[]$ |
| 6069.b4 |
6069b6 |
6069.b |
6069b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( - 3 \cdot 7^{8} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.90 |
2B |
$5712$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$18432$ |
$1.490812$ |
$-4354703137/17294403$ |
$1.04266$ |
$4.73610$ |
$[1, 1, 1, -9832, -1056292]$ |
\(y^2+xy+y=x^3+x^2-9832x-1056292\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$ |
$[]$ |
| 6069.b5 |
6069b2 |
6069.b |
6069b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.10 |
2Cs |
$2856$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$4608$ |
$0.797665$ |
$7189057/3969$ |
$1.14862$ |
$3.76392$ |
$[1, 1, 1, -1162, -3754]$ |
\(y^2+xy+y=x^3+x^2-1162x-3754\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$ |
$[]$ |
| 6069.b6 |
6069b1 |
6069.b |
6069b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( - 3^{2} \cdot 7 \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.1 |
2B |
$5712$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$2304$ |
$0.451091$ |
$103823/63$ |
$0.97868$ |
$3.27745$ |
$[1, 1, 1, 283, -286]$ |
\(y^2+xy+y=x^3+x^2+283x-286\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$ |
$[]$ |
| 6069.c1 |
6069d1 |
6069.c |
6069d |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( - 3 \cdot 7^{4} \cdot 17^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$9216$ |
$1.075993$ |
$-16777216/122451$ |
$1.06893$ |
$4.16094$ |
$[0, 1, 1, -1541, -86446]$ |
\(y^2+y=x^3+x^2-1541x-86446\) |
102.2.0.? |
$[]$ |
| 6069.d1 |
6069e1 |
6069.d |
6069e |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( - 3^{17} \cdot 7^{4} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$0.225098426$ |
$1$ |
|
$6$ |
$156672$ |
$2.544430$ |
$5009339741732864/5271114033171$ |
$1.04955$ |
$6.10144$ |
$[0, 1, 1, 1030189, 364409024]$ |
\(y^2+y=x^3+x^2+1030189x+364409024\) |
102.2.0.? |
$[(334, 27310)]$ |
| 6069.e1 |
6069c1 |
6069.e |
6069c |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 17^{2} \) |
\( - 3 \cdot 7^{2} \cdot 17^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$13824$ |
$1.228355$ |
$841232384/722211$ |
$0.90829$ |
$4.31063$ |
$[0, -1, 1, 5684, -116577]$ |
\(y^2+y=x^3-x^2+5684x-116577\) |
102.2.0.? |
$[]$ |
