Atkin-Lehner |
7+ 31+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
13237a |
Isogeny class |
Conductor |
13237 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
3400 |
Modular degree for the optimal curve |
Δ |
-31782037 = -1 · 75 · 31 · 61 |
Discriminant |
Eigenvalues |
-1 2 2 7+ -2 5 6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-62,304] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:24:1] |
Generators of the group modulo torsion |
j |
-26383748833/31782037 |
j-invariant |
L |
4.7142174336977 |
L(r)(E,1)/r! |
Ω |
1.8839135392321 |
Real period |
R |
2.5023533912386 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
119133d1 92659i1 |
Quadratic twists by: -3 -7 |