Atkin-Lehner |
3+ 5+ 31- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
85095b |
Isogeny class |
Conductor |
85095 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
203008 |
Modular degree for the optimal curve |
Δ |
-62325439453125 = -1 · 33 · 513 · 31 · 61 |
Discriminant |
Eigenvalues |
1 3+ 5+ 2 -3 2 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-15735,-845450] |
[a1,a2,a3,a4,a6] |
j |
-15957899106451947/2308349609375 |
j-invariant |
L |
3.8059142116006 |
L(r)(E,1)/r! |
Ω |
0.21143967844524 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85095e1 |
Quadratic twists by: -3 |