Atkin-Lehner |
2- 3- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69192bf |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1428480 |
Modular degree for the optimal curve |
Δ |
-4297588298227507968 = -1 · 28 · 39 · 318 |
Discriminant |
Eigenvalues |
2- 3- -4 0 2 1 0 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-357492,-129292940] |
[a1,a2,a3,a4,a6] |
Generators |
[96277860:2769630710:79507] |
Generators of the group modulo torsion |
j |
-31744/27 |
j-invariant |
L |
5.3541462538618 |
L(r)(E,1)/r! |
Ω |
0.094245502008686 |
Real period |
R |
14.202657263337 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999986919 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064e1 69192bm1 |
Quadratic twists by: -3 -31 |