Atkin-Lehner |
2+ 3- 5+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970bb |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
760320 |
Modular degree for the optimal curve |
Δ |
-2668434853198950 = -1 · 2 · 312 · 52 · 114 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 5 11- -1 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-80589,-9156314] |
[a1,a2,a3,a4,a6] |
j |
-3953416087371289/182257690950 |
j-invariant |
L |
3.3911328504003 |
L(r)(E,1)/r! |
Ω |
0.14129720273362 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
68970cn1 |
Quadratic twists by: -11 |