Atkin-Lehner |
2- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
27968by |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3328 |
Modular degree for the optimal curve |
Δ |
-643264 = -1 · 26 · 19 · 232 |
Discriminant |
Eigenvalues |
2- -2 3 3 -3 -2 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-19,-57] |
[a1,a2,a3,a4,a6] |
Generators |
[6:9:1] |
Generators of the group modulo torsion |
j |
-12487168/10051 |
j-invariant |
L |
4.8716566013309 |
L(r)(E,1)/r! |
Ω |
1.1005427539553 |
Real period |
R |
2.2132972952765 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27968bp1 13984d1 |
Quadratic twists by: -4 8 |