Atkin-Lehner |
3- 5+ 7- 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
128205w |
Isogeny class |
Conductor |
128205 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
229376 |
Modular degree for the optimal curve |
Δ |
218076705 = 37 · 5 · 72 · 11 · 37 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7- 11+ -2 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-56093,5127396] |
[a1,a2,a3,a4,a6] |
Generators |
[138:-49:1] [218:1686:1] |
Generators of the group modulo torsion |
j |
26774102938310281/299145 |
j-invariant |
L |
7.3293535833475 |
L(r)(E,1)/r! |
Ω |
1.2450753442543 |
Real period |
R |
5.8866747442712 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999469 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42735e1 |
Quadratic twists by: -3 |