Atkin-Lehner |
3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347v |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
887040 |
Modular degree for the optimal curve |
Δ |
-4721196362873846427 = -1 · 33 · 118 · 138 |
Discriminant |
Eigenvalues |
0 3- 0 1 11- 13+ 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-1499593,714008455] |
[a1,a2,a3,a4,a6] |
Generators |
[745:3295:1] |
Generators of the group modulo torsion |
j |
-360448000/4563 |
j-invariant |
L |
7.0996249755032 |
L(r)(E,1)/r! |
Ω |
0.24488209734144 |
Real period |
R |
2.4160010922402 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996328 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347w1 4719l1 |
Quadratic twists by: -11 13 |