Atkin-Lehner |
3- 5+ 7- 37- |
Signs for the Atkin-Lehner involutions |
Class |
81585t |
Isogeny class |
Conductor |
81585 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
702846661116796875 = 310 · 58 · 77 · 37 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7- 0 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-660848,-202638544] |
[a1,a2,a3,a4,a6] |
Generators |
[-474:2221:1] [-3522:15203:8] |
Generators of the group modulo torsion |
j |
372144896498089/8194921875 |
j-invariant |
L |
6.699990986682 |
L(r)(E,1)/r! |
Ω |
0.16767031938461 |
Real period |
R |
4.9949142842597 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999366 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27195t3 11655o4 |
Quadratic twists by: -3 -7 |