Atkin-Lehner |
2- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
682b |
Isogeny class |
Conductor |
682 |
Conductor |
∏ cp |
57 |
Product of Tamagawa factors cp |
deg |
456 |
Modular degree for the optimal curve |
Δ |
-21632647168 = -1 · 219 · 113 · 31 |
Discriminant |
Eigenvalues |
2- 0 -2 -3 11- -4 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,359,-6663] |
[a1,a2,a3,a4,a6] |
Generators |
[15:36:1] |
Generators of the group modulo torsion |
j |
5130275528223/21632647168 |
j-invariant |
L |
2.6265637235401 |
L(r)(E,1)/r! |
Ω |
0.61155331209393 |
Real period |
R |
0.075349220442432 |
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 |
5456g1 21824b1 6138c1 17050d1 |
Quadratic twists by: -4 8 -3 5 |