Atkin-Lehner |
3- 5- 37+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
68265j |
Isogeny class |
Conductor |
68265 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
190464 |
Modular degree for the optimal curve |
Δ |
15983609765625 = 36 · 58 · 372 · 41 |
Discriminant |
Eigenvalues |
1 3- 5- 2 6 -6 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-8649,244768] |
[a1,a2,a3,a4,a6] |
Generators |
[-48:764:1] |
Generators of the group modulo torsion |
j |
98157190604689/21925390625 |
j-invariant |
L |
8.5064931053373 |
L(r)(E,1)/r! |
Ω |
0.65720626843443 |
Real period |
R |
1.6179268053842 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999981242 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7585a1 |
Quadratic twists by: -3 |