Atkin-Lehner |
3- 23+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
2139c |
Isogeny class |
Conductor |
2139 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1296 |
Modular degree for the optimal curve |
Δ |
519777 = 36 · 23 · 31 |
Discriminant |
Eigenvalues |
-1 3- -2 0 -4 -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-10829,432840] |
[a1,a2,a3,a4,a6] |
j |
140440148435570257/519777 |
j-invariant |
L |
0.73524009921284 |
L(r)(E,1)/r! |
Ω |
1.9606402645676 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
34224bb1 6417h1 53475c1 104811e1 |
Quadratic twists by: -4 -3 5 -7 |