Atkin-Lehner |
2- 3+ 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936j |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
Δ |
-684120119795712 = -1 · 213 · 33 · 313 · 473 |
Discriminant |
Eigenvalues |
2- 3+ 0 1 0 -4 6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3888,1263168] |
[a1,a2,a3,a4,a6] |
Generators |
[64:1128:1] |
Generators of the group modulo torsion |
j |
-1587282504625/167021513622 |
j-invariant |
L |
5.2980556255541 |
L(r)(E,1)/r! |
Ω |
0.4186548216876 |
Real period |
R |
1.0545791246117 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002108 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742k2 |
Quadratic twists by: -4 |