Atkin-Lehner |
3- 5+ 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
9735h |
Isogeny class |
Conductor |
9735 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
91265625 = 32 · 56 · 11 · 59 |
Discriminant |
Eigenvalues |
1 3- 5+ -4 11- 2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-139,-439] |
[a1,a2,a3,a4,a6] |
Generators |
[61:437:1] |
Generators of the group modulo torsion |
j |
293946977449/91265625 |
j-invariant |
L |
5.2201852784487 |
L(r)(E,1)/r! |
Ω |
1.4254273187182 |
Real period |
R |
3.6621897236702 |
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 |
29205m1 48675f1 107085o1 |
Quadratic twists by: -3 5 -11 |