Atkin-Lehner |
3- 5+ 7+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
77805k |
Isogeny class |
Conductor |
77805 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
7089980625 = 38 · 54 · 7 · 13 · 19 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 0 13+ -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2993,63632] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:358:1] [-15:331:1] |
Generators of the group modulo torsion |
j |
4066120948681/9725625 |
j-invariant |
L |
6.1696643355316 |
L(r)(E,1)/r! |
Ω |
1.3297087792123 |
Real period |
R |
2.3199306615248 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999911 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25935o1 |
Quadratic twists by: -3 |