Atkin-Lehner |
2+ 3- 7- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
86688v |
Isogeny class |
Conductor |
86688 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
53248 |
Modular degree for the optimal curve |
Δ |
-6291468288 = -1 · 212 · 36 · 72 · 43 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 3 5 -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-936,-11664] |
[a1,a2,a3,a4,a6] |
Generators |
[36:36:1] |
Generators of the group modulo torsion |
j |
-30371328/2107 |
j-invariant |
L |
6.3569651505106 |
L(r)(E,1)/r! |
Ω |
0.42985044274112 |
Real period |
R |
1.8485979425118 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999997166 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86688bq1 9632f1 |
Quadratic twists by: -4 -3 |