Atkin-Lehner |
3- 5+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
81225z |
Isogeny class |
Conductor |
81225 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-8038229823984375 = -1 · 37 · 57 · 196 |
Discriminant |
Eigenvalues |
1 3- 5+ 0 4 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1692,4314091] |
[a1,a2,a3,a4,a6] |
Generators |
[-986:13489:8] |
Generators of the group modulo torsion |
j |
-1/15 |
j-invariant |
L |
7.8624928353941 |
L(r)(E,1)/r! |
Ω |
0.33185825612467 |
Real period |
R |
2.9615403161277 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999966547 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27075g1 16245d1 225c1 |
Quadratic twists by: -3 5 -19 |