Atkin-Lehner |
3+ 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
12705c |
Isogeny class |
Conductor |
12705 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
55246129785 = 34 · 5 · 7 · 117 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- 11- 2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1333,14392] |
[a1,a2,a3,a4,a6] |
Generators |
[424:8500:1] |
Generators of the group modulo torsion |
j |
148035889/31185 |
j-invariant |
L |
4.1756489444574 |
L(r)(E,1)/r! |
Ω |
1.0568583800707 |
Real period |
R |
1.9755007024583 |
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 |
38115bd1 63525bi1 88935cg1 1155a1 |
Quadratic twists by: -3 5 -7 -11 |