Atkin-Lehner |
3- 71- |
Signs for the Atkin-Lehner involutions |
Class |
45369a |
Isogeny class |
Conductor |
45369 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-59673083359203351 = -1 · 38 · 717 |
Discriminant |
Eigenvalues |
-1 3- -2 -2 0 2 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,21739,11682596] |
[a1,a2,a3,a4,a6] |
Generators |
[-48:3268:1] |
Generators of the group modulo torsion |
j |
12167/639 |
j-invariant |
L |
2.5531074523784 |
L(r)(E,1)/r! |
Ω |
0.26696544764565 |
Real period |
R |
4.7817188982436 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000031 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15123a1 639a1 |
Quadratic twists by: -3 -71 |