Atkin-Lehner |
2+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
112112b |
Isogeny class |
Conductor |
112112 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
157248 |
Modular degree for the optimal curve |
Δ |
-2229087132272 = -1 · 24 · 78 · 11 · 133 |
Discriminant |
Eigenvalues |
2+ -1 2 7+ 11- 13+ 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2172,82447] |
[a1,a2,a3,a4,a6] |
j |
-12291328/24167 |
j-invariant |
L |
0.73181717402005 |
L(r)(E,1)/r! |
Ω |
0.73181626813343 |
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 |
56056a1 112112s1 |
Quadratic twists by: -4 -7 |