Atkin-Lehner |
2- 3- 5- 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85140o |
Isogeny class |
Conductor |
85140 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
350208 |
Modular degree for the optimal curve |
Δ |
2155106250000 = 24 · 36 · 58 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3- 5- -5 11+ -2 -6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-59997,5655989] |
[a1,a2,a3,a4,a6] |
Generators |
[193:-1125:1] [-187:3215:1] |
Generators of the group modulo torsion |
j |
2047692815359744/184765625 |
j-invariant |
L |
9.9513612269515 |
L(r)(E,1)/r! |
Ω |
0.78752177948498 |
Real period |
R |
0.26325624378121 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999217 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9460b1 |
Quadratic twists by: -3 |