Atkin-Lehner |
3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347t |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1290240 |
Modular degree for the optimal curve |
Δ |
-490467841536173787 = -1 · 35 · 114 · 1310 |
Discriminant |
Eigenvalues |
-2 3+ 0 3 11- 13+ 8 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-170408,-43168786] |
[a1,a2,a3,a4,a6] |
j |
-7744000000/6940323 |
j-invariant |
L |
1.3592338255061 |
L(r)(E,1)/r! |
Ω |
0.11326948596205 |
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 |
61347p1 4719h1 |
Quadratic twists by: -11 13 |