Atkin-Lehner |
3+ 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033f |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1077120 |
Modular degree for the optimal curve |
Δ |
-3.7181802674379E+19 |
Discriminant |
Eigenvalues |
0 3+ -3 7+ 11- 13- 8 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,185453,291698472] |
[a1,a2,a3,a4,a6] |
Generators |
[362908:14021860:343] |
Generators of the group modulo torsion |
j |
27195441152/1433519451 |
j-invariant |
L |
2.8388323085826 |
L(r)(E,1)/r! |
Ω |
0.15617069147086 |
Real period |
R |
9.0888766702817 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099bc1 33033m1 |
Quadratic twists by: -3 -11 |