Atkin-Lehner |
7- 11- 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
119119j |
Isogeny class |
Conductor |
119119 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
864000 |
Modular degree for the optimal curve |
Δ |
-156395019249239771 = -1 · 76 · 115 · 134 · 172 |
Discriminant |
Eigenvalues |
0 -1 1 7- 11- 13- 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-491535,134163315] |
[a1,a2,a3,a4,a6] |
Generators |
[415:1215:1] [-1542:119115:8] |
Generators of the group modulo torsion |
j |
-111634825505112064/1329335729579 |
j-invariant |
L |
8.7657035915402 |
L(r)(E,1)/r! |
Ω |
0.3253928319619 |
Real period |
R |
0.33673542902754 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001924 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2431a1 |
Quadratic twists by: -7 |