Atkin-Lehner |
2+ 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208d |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-57446986447872 = -1 · 210 · 34 · 77 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- -4 0 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,5472,327888] |
[a1,a2,a3,a4,a6] |
Generators |
[54:-882:1] [-36:288:1] |
Generators of the group modulo torsion |
j |
150381500/476847 |
j-invariant |
L |
8.9186514117708 |
L(r)(E,1)/r! |
Ω |
0.4425867443078 |
Real period |
R |
2.5188992684754 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999776 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34104n1 9744d1 |
Quadratic twists by: -4 -7 |