Atkin-Lehner |
2+ 3+ 11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
84216b |
Isogeny class |
Conductor |
84216 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
591360 |
Modular degree for the optimal curve |
Δ |
15597314659263744 = 28 · 34 · 1110 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ -2 1 11- 1 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-136649,-18445491] |
[a1,a2,a3,a4,a6] |
j |
42499072/2349 |
j-invariant |
L |
1.9933387931413 |
L(r)(E,1)/r! |
Ω |
0.24916735812613 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84216p1 |
Quadratic twists by: -11 |