Atkin-Lehner |
2+ 7- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
115192m |
Isogeny class |
Conductor |
115192 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1419264 |
Modular degree for the optimal curve |
Δ |
6859597373489168 = 24 · 76 · 118 · 17 |
Discriminant |
Eigenvalues |
2+ 2 4 7- 11- -1 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-345616,-77989107] |
[a1,a2,a3,a4,a6] |
Generators |
[-42270:39669:125] |
Generators of the group modulo torsion |
j |
1331205255424/2000033 |
j-invariant |
L |
14.675503560574 |
L(r)(E,1)/r! |
Ω |
0.19692015864892 |
Real period |
R |
6.2104288123753 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000024834 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
115192z1 |
Quadratic twists by: -11 |