Atkin-Lehner |
3- 61- |
Signs for the Atkin-Lehner involutions |
Class |
33489i |
Isogeny class |
Conductor |
33489 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
57600 |
Modular degree for the optimal curve |
Δ |
-120627009621 = -1 · 312 · 613 |
Discriminant |
Eigenvalues |
1 3- -3 -3 -5 -3 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-9756,-368847] |
[a1,a2,a3,a4,a6] |
Generators |
[168:1563:1] |
Generators of the group modulo torsion |
j |
-620650477/729 |
j-invariant |
L |
2.1722066670588 |
L(r)(E,1)/r! |
Ω |
0.24017010089707 |
Real period |
R |
2.2611127061038 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11163f1 33489k1 |
Quadratic twists by: -3 61 |