Atkin-Lehner |
2- 3+ 7+ 19- 29- |
Signs for the Atkin-Lehner involutions |
Class |
69426z |
Isogeny class |
Conductor |
69426 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
164864 |
Modular degree for the optimal curve |
Δ |
-226926379008 = -1 · 214 · 33 · 72 · 192 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -4 7+ -4 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-242,23025] |
[a1,a2,a3,a4,a6] |
Generators |
[-234:645:8] [-15:159:1] |
Generators of the group modulo torsion |
j |
-57825915363/8404680704 |
j-invariant |
L |
11.637334520325 |
L(r)(E,1)/r! |
Ω |
0.81345828717894 |
Real period |
R |
0.51092858301826 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999971 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69426c1 |
Quadratic twists by: -3 |