Atkin-Lehner |
2+ 3- 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
83304j |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
269568 |
Modular degree for the optimal curve |
Δ |
215923968 = 28 · 36 · 13 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 4 3 2 13+ -7 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-62508,6015220] |
[a1,a2,a3,a4,a6] |
Generators |
[140:90:1] |
Generators of the group modulo torsion |
j |
144731488592896/1157 |
j-invariant |
L |
10.593582724852 |
L(r)(E,1)/r! |
Ω |
1.2279086212977 |
Real period |
R |
1.0784172511468 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004283 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9256c1 |
Quadratic twists by: -3 |