Atkin-Lehner |
2- 5+ 13- 67- |
Signs for the Atkin-Lehner involutions |
Class |
69680u |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
587520 |
Modular degree for the optimal curve |
Δ |
-128418649735168000 = -1 · 229 · 53 · 134 · 67 |
Discriminant |
Eigenvalues |
2- 0 5+ -1 3 13- 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-712643,232197058] |
[a1,a2,a3,a4,a6] |
j |
-9771918471960616089/31352209408000 |
j-invariant |
L |
2.6464979659087 |
L(r)(E,1)/r! |
Ω |
0.33081224508198 |
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 |
8710d1 |
Quadratic twists by: -4 |