Atkin-Lehner |
2+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
12272c |
Isogeny class |
Conductor |
12272 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
200960 |
Modular degree for the optimal curve |
Δ |
-2082214660887296 = -1 · 28 · 1310 · 59 |
Discriminant |
Eigenvalues |
2+ 3 -3 -1 -6 13- -6 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-237199,-44519074] |
[a1,a2,a3,a4,a6] |
j |
-5765305272706770768/8133651019091 |
j-invariant |
L |
2.1631399195416 |
L(r)(E,1)/r! |
Ω |
0.10815699597708 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6136c1 49088q1 110448v1 |
Quadratic twists by: -4 8 -3 |