Atkin-Lehner |
2+ 3+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68952f |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
680064 |
Modular degree for the optimal curve |
Δ |
-69241178309112576 = -1 · 28 · 323 · 132 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -2 -4 13+ 17- 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-328865,-73575867] |
[a1,a2,a3,a4,a6] |
j |
-90918304699515904/1600434040059 |
j-invariant |
L |
0.39831014086537 |
L(r)(E,1)/r! |
Ω |
0.099577534552011 |
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 |
68952v1 |
Quadratic twists by: 13 |