| 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 |
| 66.a1 |
66a3 |
66.a |
66a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{6} \cdot 3 \cdot 11^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.4, 3.8.0.2 |
2B, 3B.1.2 |
$264$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$12$ |
$-0.110077$ |
$57736239625/255552$ |
$0.99775$ |
$5.91437$ |
$[1, 0, 1, -81, -284]$ |
\(y^2+xy+y=x^3-81x-284\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.d.1, 24.48.0-24.bx.1.11, $\ldots$ |
$[]$ |
| 66.a2 |
66a4 |
66.a |
66a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 11 \) |
\( - 2^{3} \cdot 3^{2} \cdot 11^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.5, 3.8.0.2 |
2B, 3B.1.2 |
$264$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$24$ |
$0.236497$ |
$-7357983625/127552392$ |
$1.05287$ |
$6.24195$ |
$[1, 0, 1, -41, -556]$ |
\(y^2+xy+y=x^3-41x-556\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.a.1, 24.48.0-24.p.1.13, $\ldots$ |
$[]$ |
| 66.a3 |
66a1 |
66.a |
66a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{2} \cdot 3^{3} \cdot 11 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.4, 3.8.0.1 |
2B, 3B.1.1 |
$264$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$4$ |
$-0.659383$ |
$18609625/1188$ |
$0.92581$ |
$3.99536$ |
$[1, 0, 1, -6, 4]$ |
\(y^2+xy+y=x^3-6x+4\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.d.1, 24.48.0-24.bx.1.15, $\ldots$ |
$[]$ |
| 66.a4 |
66a2 |
66.a |
66a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 11 \) |
\( - 2 \cdot 3^{6} \cdot 11^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.5, 3.8.0.1 |
2B, 3B.1.1 |
$264$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$8$ |
$-0.312809$ |
$9938375/176418$ |
$1.01160$ |
$4.65484$ |
$[1, 0, 1, 4, 20]$ |
\(y^2+xy+y=x^3+4x+20\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.a.1, 24.48.0-24.p.1.15, $\ldots$ |
$[]$ |
| 66.b1 |
66b3 |
66.b |
66b |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2 \cdot 3 \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.102 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$16$ |
$-0.094954$ |
$4824238966273/66$ |
$1.02376$ |
$6.97066$ |
$[1, 1, 1, -352, -2689]$ |
\(y^2+xy+y=x^3+x^2-352x-2689\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 132.12.0.?, 264.48.0.? |
$[]$ |
| 66.b2 |
66b2 |
66.b |
66b |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.4 |
2Cs |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$8$ |
$-0.441527$ |
$1180932193/4356$ |
$0.96736$ |
$4.98599$ |
$[1, 1, 1, -22, -49]$ |
\(y^2+xy+y=x^3+x^2-22x-49\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 132.24.0.?, 264.48.0.? |
$[]$ |
| 66.b3 |
66b4 |
66.b |
66b |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 11 \) |
\( - 2 \cdot 3^{4} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.59 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$16$ |
$-0.094954$ |
$-192100033/2371842$ |
$1.02507$ |
$5.29392$ |
$[1, 1, 1, -12, -81]$ |
\(y^2+xy+y=x^3+x^2-12x-81\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 264.48.0.? |
$[]$ |
| 66.b4 |
66b1 |
66.b |
66b |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3 \cdot 11 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.53 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-0.788101$ |
$912673/528$ |
$1.18336$ |
$3.27572$ |
$[1, 1, 1, -2, -1]$ |
\(y^2+xy+y=x^3+x^2-2x-1\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 66.6.0.a.1, 132.24.0.?, $\ldots$ |
$[]$ |
| 66.c1 |
66c3 |
66.c |
66c |
$4$ |
$10$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{2} \cdot 3 \cdot 11^{5} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 5$ |
8.6.0.4, 5.24.0.3 |
2B, 5B.1.2 |
$1320$ |
$288$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$100$ |
$0.747853$ |
$112763292123580561/1932612$ |
$1.06379$ |
$9.37167$ |
$[1, 0, 0, -10065, -389499]$ |
\(y^2+xy=x^3-10065x-389499\) |
2.3.0.a.1, 5.24.0-5.a.2.2, 8.6.0.d.1, 10.72.0-10.a.1.2, 40.144.1-40.t.1.4, $\ldots$ |
$[]$ |
| 66.c2 |
66c4 |
66.c |
66c |
$4$ |
$10$ |
\( 2 \cdot 3 \cdot 11 \) |
\( - 2 \cdot 3^{2} \cdot 11^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 5$ |
8.6.0.5, 5.24.0.3 |
2B, 5B.1.2 |
$1320$ |
$288$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$200$ |
$1.094427$ |
$-112427521449300721/466873642818$ |
$1.06387$ |
$9.37267$ |
$[1, 0, 0, -10055, -390309]$ |
\(y^2+xy=x^3-10055x-390309\) |
2.3.0.a.1, 5.24.0-5.a.2.2, 8.6.0.a.1, 10.72.0-10.a.1.2, 40.144.1-40.c.2.13, $\ldots$ |
$[]$ |
| 66.c3 |
66c1 |
66.c |
66c |
$4$ |
$10$ |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{10} \cdot 3^{5} \cdot 11 \) |
$0$ |
$\Z/10\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 5$ |
8.6.0.4, 5.24.0.1 |
2B, 5B.1.1 |
$1320$ |
$288$ |
$5$ |
$1$ |
$1$ |
|
$9$ |
$20$ |
$-0.056866$ |
$10091699281/2737152$ |
$1.07340$ |
$5.49806$ |
$[1, 0, 0, -45, 81]$ |
\(y^2+xy=x^3-45x+81\) |
2.3.0.a.1, 5.24.0-5.a.1.2, 8.6.0.d.1, 10.72.0-10.a.2.1, 40.144.1-40.t.2.4, $\ldots$ |
$[]$ |
| 66.c4 |
66c2 |
66.c |
66c |
$4$ |
$10$ |
\( 2 \cdot 3 \cdot 11 \) |
\( - 2^{5} \cdot 3^{10} \cdot 11^{2} \) |
$0$ |
$\Z/10\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 5$ |
8.6.0.5, 5.24.0.1 |
2B, 5B.1.1 |
$1320$ |
$288$ |
$5$ |
$1$ |
$1$ |
|
$8$ |
$40$ |
$0.289708$ |
$168105213359/228637728$ |
$1.10021$ |
$6.24112$ |
$[1, 0, 0, 115, 561]$ |
\(y^2+xy=x^3+115x+561\) |
2.3.0.a.1, 5.24.0-5.a.1.2, 8.6.0.a.1, 10.72.0-10.a.2.1, 40.144.1-40.c.1.13, $\ldots$ |
$[]$ |
