Atkin-Lehner |
2- 3+ 7+ 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
33306m |
Isogeny class |
Conductor |
33306 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
1398852 = 22 · 32 · 72 · 13 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 0 13+ 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-144,-723] |
[a1,a2,a3,a4,a6] |
Generators |
[-58:37:8] |
Generators of the group modulo torsion |
j |
330369290497/1398852 |
j-invariant |
L |
5.962195451984 |
L(r)(E,1)/r! |
Ω |
1.3784907470008 |
Real period |
R |
2.1625808751187 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99918e1 |
Quadratic twists by: -3 |