Atkin-Lehner |
2+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
4312d |
Isogeny class |
Conductor |
4312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-25510067968 = -1 · 28 · 77 · 112 |
Discriminant |
Eigenvalues |
2+ 2 -2 7- 11+ -4 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-604,9780] |
[a1,a2,a3,a4,a6] |
j |
-810448/847 |
j-invariant |
L |
2.1681114075415 |
L(r)(E,1)/r! |
Ω |
1.0840557037707 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8624k1 34496bt1 38808cm1 107800bt1 |
Quadratic twists by: -4 8 -3 5 |