Atkin-Lehner |
2+ 3- 5- 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69090z |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-79624843200 = -1 · 26 · 32 · 52 · 76 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7- 2 -4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,807,-10244] |
[a1,a2,a3,a4,a6] |
Generators |
[32:204:1] |
Generators of the group modulo torsion |
j |
494913671/676800 |
j-invariant |
L |
6.6845348924642 |
L(r)(E,1)/r! |
Ω |
0.57714799117113 |
Real period |
R |
1.4477514855566 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994495 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1410b1 |
Quadratic twists by: -7 |