Atkin-Lehner |
3- 7+ 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
128037h |
Isogeny class |
Conductor |
128037 |
Conductor |
∏ cp |
114 |
Product of Tamagawa factors cp |
deg |
6518976 |
Modular degree for the optimal curve |
Δ |
-5340036329678961729 = -1 · 319 · 74 · 134 · 67 |
Discriminant |
Eigenvalues |
-1 3- -1 7+ -2 13+ -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-22447881,40934821122] |
[a1,a2,a3,a4,a6] |
Generators |
[-4581:220554:1] [2727:-2214:1] |
Generators of the group modulo torsion |
j |
-521023854618651377185969/2224088433852129 |
j-invariant |
L |
8.2239417961542 |
L(r)(E,1)/r! |
Ω |
0.21274123560161 |
Real period |
R |
0.33909665023351 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999941916 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128037e1 |
Quadratic twists by: -7 |