Atkin-Lehner |
7- 37+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
85211h |
Isogeny class |
Conductor |
85211 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
3768 |
Modular degree for the optimal curve |
Δ |
-85211 = -1 · 72 · 37 · 47 |
Discriminant |
Eigenvalues |
0 -1 -2 7- 0 1 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-9,-15] |
[a1,a2,a3,a4,a6] |
Generators |
[9:23:1] |
Generators of the group modulo torsion |
j |
-1835008/1739 |
j-invariant |
L |
3.1070514577016 |
L(r)(E,1)/r! |
Ω |
1.3147004933748 |
Real period |
R |
2.3633150460195 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002252 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85211a1 |
Quadratic twists by: -7 |