Atkin-Lehner |
3+ 13+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
8541a |
Isogeny class |
Conductor |
8541 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4416 |
Modular degree for the optimal curve |
Δ |
-242829171 = -1 · 39 · 132 · 73 |
Discriminant |
Eigenvalues |
2 3+ -3 -2 4 13+ 1 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,81,695] |
[a1,a2,a3,a4,a6] |
Generators |
[66:347:8] |
Generators of the group modulo torsion |
j |
2985984/12337 |
j-invariant |
L |
6.7626280849862 |
L(r)(E,1)/r! |
Ω |
1.2546509995795 |
Real period |
R |
1.3475117955617 |
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 |
8541b1 111033b1 |
Quadratic twists by: -3 13 |