Atkin-Lehner |
3+ 7- 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
85701n |
Isogeny class |
Conductor |
85701 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
14848 |
Modular degree for the optimal curve |
Δ |
16197489 = 34 · 73 · 11 · 53 |
Discriminant |
Eigenvalues |
-1 3+ -2 7- 11- 2 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-64,-64] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:7:1] |
Generators of the group modulo torsion |
j |
84604519/47223 |
j-invariant |
L |
2.5176095609585 |
L(r)(E,1)/r! |
Ω |
1.8119084761451 |
Real period |
R |
1.3894794321995 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001299 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85701bb1 |
Quadratic twists by: -7 |