Atkin-Lehner |
2- 3+ 7+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
41118j |
Isogeny class |
Conductor |
41118 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
-189140168448 = -1 · 28 · 34 · 7 · 114 · 89 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 11- -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,406,20855] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:91:1] [-15:115:1] |
Generators of the group modulo torsion |
j |
7400055134303/189140168448 |
j-invariant |
L |
10.191196560388 |
L(r)(E,1)/r! |
Ω |
0.75748443945249 |
Real period |
R |
3.3635003009944 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
123354k1 |
Quadratic twists by: -3 |