Atkin-Lehner |
3- 11+ 19- 53- |
Signs for the Atkin-Lehner involutions |
Class |
99693d |
Isogeny class |
Conductor |
99693 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
19968 |
Modular degree for the optimal curve |
Δ |
-72676197 = -1 · 38 · 11 · 19 · 53 |
Discriminant |
Eigenvalues |
-1 3- 0 -1 11+ 1 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-545,5046] |
[a1,a2,a3,a4,a6] |
Generators |
[14:-3:1] [-13:105:1] |
Generators of the group modulo torsion |
j |
-24515367625/99693 |
j-invariant |
L |
7.1504512064259 |
L(r)(E,1)/r! |
Ω |
1.9523132631762 |
Real period |
R |
1.8312766043015 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000254 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33231c1 |
Quadratic twists by: -3 |