Atkin-Lehner |
2- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
27968bz |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
41472 |
Modular degree for the optimal curve |
Δ |
7575076864 = 215 · 19 · 233 |
Discriminant |
Eigenvalues |
2- 3 -3 2 -5 -2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1324,-18064] |
[a1,a2,a3,a4,a6] |
Generators |
[-537:541:27] |
Generators of the group modulo torsion |
j |
7833173256/231173 |
j-invariant |
L |
8.1083225272008 |
L(r)(E,1)/r! |
Ω |
0.79288710910287 |
Real period |
R |
5.113163295324 |
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 |
27968bq1 13984e1 |
Quadratic twists by: -4 8 |