Atkin-Lehner |
3- 7+ 11+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
15477b |
Isogeny class |
Conductor |
15477 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
3648 |
Modular degree for the optimal curve |
Δ |
-9332631 = -1 · 33 · 7 · 11 · 672 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ 11+ -2 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,21,144] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:9:1] [0:12:1] |
Generators of the group modulo torsion |
j |
1021147343/9332631 |
j-invariant |
L |
4.7104236338426 |
L(r)(E,1)/r! |
Ω |
1.689767663709 |
Real period |
R |
1.8584107685365 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
46431h1 108339c1 |
Quadratic twists by: -3 -7 |