Atkin-Lehner |
2- 3+ 7- 11- 29- |
Signs for the Atkin-Lehner involutions |
Class |
13398bd |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
4716096 = 26 · 3 · 7 · 112 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 11- -6 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-42,-9] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:11:1] |
Generators of the group modulo torsion |
j |
8205738913/4716096 |
j-invariant |
L |
7.0082556292347 |
L(r)(E,1)/r! |
Ω |
2.0832603120803 |
Real period |
R |
1.1213602045786 |
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 |
107184cg1 40194r1 93786dc1 |
Quadratic twists by: -4 -3 -7 |