Atkin-Lehner |
3+ 5+ 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
6405c |
Isogeny class |
Conductor |
6405 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2400 |
Modular degree for the optimal curve |
Δ |
-4707675 = -1 · 32 · 52 · 73 · 61 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7- -6 -2 -1 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-36,146] |
[a1,a2,a3,a4,a6] |
Generators |
[28:-143:1] [-6:10:1] |
Generators of the group modulo torsion |
j |
-5304438784/4707675 |
j-invariant |
L |
2.4287628333776 |
L(r)(E,1)/r! |
Ω |
2.2313545376349 |
Real period |
R |
0.090705846770508 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102480bt1 19215v1 32025t1 44835be1 |
Quadratic twists by: -4 -3 5 -7 |