Atkin-Lehner |
2+ 3+ 5- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
32040a |
Isogeny class |
Conductor |
32040 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
58368 |
Modular degree for the optimal curve |
Δ |
-240300000000 = -1 · 28 · 33 · 58 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -4 -6 0 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7212,236916] |
[a1,a2,a3,a4,a6] |
Generators |
[-98:50:1] [102:-750:1] |
Generators of the group modulo torsion |
j |
-6001877634048/34765625 |
j-invariant |
L |
7.9483169410723 |
L(r)(E,1)/r! |
Ω |
0.99430497122716 |
Real period |
R |
0.12490378284139 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64080b1 32040f1 |
Quadratic twists by: -4 -3 |