Atkin-Lehner |
2- 3+ 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936n |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
29952 |
Modular degree for the optimal curve |
Δ |
-107421696 = -1 · 213 · 32 · 31 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -3 4 1 0 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,8,496] |
[a1,a2,a3,a4,a6] |
Generators |
[4:-24:1] |
Generators of the group modulo torsion |
j |
12167/26226 |
j-invariant |
L |
5.5721186723467 |
L(r)(E,1)/r! |
Ω |
1.4751326715328 |
Real period |
R |
0.47217097643496 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002219 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742f1 |
Quadratic twists by: -4 |