Atkin-Lehner |
2- 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
115596d |
Isogeny class |
Conductor |
115596 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-421694208 = -1 · 28 · 33 · 132 · 192 |
Discriminant |
Eigenvalues |
2- 3+ -4 -1 -2 13+ -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-312,2340] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:66:1] [-3:57:1] |
Generators of the group modulo torsion |
j |
-2875392/361 |
j-invariant |
L |
8.5154985072813 |
L(r)(E,1)/r! |
Ω |
1.6282756112675 |
Real period |
R |
0.43581373460091 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000007056 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
115596c1 115596i1 |
Quadratic twists by: -3 13 |