Atkin-Lehner |
11+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
6413a |
Isogeny class |
Conductor |
6413 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
624 |
Modular degree for the optimal curve |
Δ |
-70543 = -1 · 113 · 53 |
Discriminant |
Eigenvalues |
1 -2 -2 -4 11+ 0 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,8,9] |
[a1,a2,a3,a4,a6] |
Generators |
[3:6:1] |
Generators of the group modulo torsion |
j |
50653/53 |
j-invariant |
L |
1.9330753726268 |
L(r)(E,1)/r! |
Ω |
2.2911211792968 |
Real period |
R |
1.6874492629151 |
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 |
102608f1 57717p1 6413b1 |
Quadratic twists by: -4 -3 -11 |