Atkin-Lehner |
3+ 5- 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
31005g |
Isogeny class |
Conductor |
31005 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
250560 |
Modular degree for the optimal curve |
Δ |
-7380340576171875 = -1 · 33 · 515 · 132 · 53 |
Discriminant |
Eigenvalues |
0 3+ 5- -4 6 13- 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-261522,51642345] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:7312:1] |
Generators of the group modulo torsion |
j |
-73262989243222622208/273345947265625 |
j-invariant |
L |
4.7875582955969 |
L(r)(E,1)/r! |
Ω |
0.41996310599112 |
Real period |
R |
1.7099924590868 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
31005d2 |
Quadratic twists by: -3 |