Atkin-Lehner |
3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347k |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
-333488476575111 = -1 · 3 · 116 · 137 |
Discriminant |
Eigenvalues |
1 3+ -2 -4 11- 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,9799,799440] |
[a1,a2,a3,a4,a6] |
j |
12167/39 |
j-invariant |
L |
0.76485658766569 |
L(r)(E,1)/r! |
Ω |
0.38242829501268 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
507c1 4719d1 |
Quadratic twists by: -11 13 |