Atkin-Lehner |
3+ 5- 7+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
69615c |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
45056 |
Modular degree for the optimal curve |
Δ |
443795625 = 33 · 54 · 7 · 13 · 172 |
Discriminant |
Eigenvalues |
-1 3+ 5- 7+ 4 13+ 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-3572,83046] |
[a1,a2,a3,a4,a6] |
Generators |
[36:-6:1] |
Generators of the group modulo torsion |
j |
186629507315523/16436875 |
j-invariant |
L |
4.3881818169381 |
L(r)(E,1)/r! |
Ω |
1.5967042717227 |
Real period |
R |
0.68706865366468 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996476 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69615a1 |
Quadratic twists by: -3 |