Atkin-Lehner |
3+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
99099d |
Isogeny class |
Conductor |
99099 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-8091716475843 = -1 · 33 · 7 · 117 · 133 |
Discriminant |
Eigenvalues |
0 3+ 0 7+ 11- 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-61710,-5901987] |
[a1,a2,a3,a4,a6] |
j |
-543338496000/169169 |
j-invariant |
L |
1.2116093084838 |
L(r)(E,1)/r! |
Ω |
0.15145114496351 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099c2 9009a1 |
Quadratic twists by: -3 -11 |