Atkin-Lehner |
2- 3- 7+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
85008ca |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
139264 |
Modular degree for the optimal curve |
Δ |
-148656549888 = -1 · 212 · 34 · 7 · 112 · 232 |
Discriminant |
Eigenvalues |
2- 3- -4 7+ 11+ -4 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1160,23604] |
[a1,a2,a3,a4,a6] |
Generators |
[-26:192:1] [-20:198:1] |
Generators of the group modulo torsion |
j |
-42180533641/36293103 |
j-invariant |
L |
9.5598666062547 |
L(r)(E,1)/r! |
Ω |
0.94203840658741 |
Real period |
R |
0.63425403753423 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5313b1 |
Quadratic twists by: -4 |