Atkin-Lehner |
7+ 11- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
61831b |
Isogeny class |
Conductor |
61831 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
168960 |
Modular degree for the optimal curve |
Δ |
-249336969355859 = -1 · 74 · 117 · 732 |
Discriminant |
Eigenvalues |
0 -1 -1 7+ 11- 0 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-42511,-3444002] |
[a1,a2,a3,a4,a6] |
Generators |
[1946:5925:8] [334:4416:1] |
Generators of the group modulo torsion |
j |
-4796028780544/140744219 |
j-invariant |
L |
5.9722270635423 |
L(r)(E,1)/r! |
Ω |
0.16595582864314 |
Real period |
R |
2.2491779561082 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999884 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5621c1 |
Quadratic twists by: -11 |