Atkin-Lehner |
2- 3- 59- |
Signs for the Atkin-Lehner involutions |
Class |
33984bw |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8960 |
Modular degree for the optimal curve |
Δ |
-44043264 = -1 · 210 · 36 · 59 |
Discriminant |
Eigenvalues |
2- 3- -1 -3 4 -6 6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,72,216] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:8:1] [1:17:1] |
Generators of the group modulo torsion |
j |
55296/59 |
j-invariant |
L |
7.8634789978318 |
L(r)(E,1)/r! |
Ω |
1.3421697662021 |
Real period |
R |
2.9293906016389 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33984l1 8496e1 3776s1 |
Quadratic twists by: -4 8 -3 |