Atkin-Lehner |
2+ 29+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68672c |
Isogeny class |
Conductor |
68672 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
-650461184 = -1 · 214 · 29 · 372 |
Discriminant |
Eigenvalues |
2+ -3 -1 -2 -5 -7 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-988,12016] |
[a1,a2,a3,a4,a6] |
Generators |
[18:-8:1] [-24:148:1] [-22:152:1] |
Generators of the group modulo torsion |
j |
-6509904336/39701 |
j-invariant |
L |
7.9534852753126 |
L(r)(E,1)/r! |
Ω |
1.6273714826156 |
Real period |
R |
0.61091500621352 |
Regulator |
r |
3 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68672r1 4292c1 |
Quadratic twists by: -4 8 |