Atkin-Lehner |
3- 5+ 7- 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
42735j |
Isogeny class |
Conductor |
42735 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7936 |
Modular degree for the optimal curve |
Δ |
-12692295 = -1 · 34 · 5 · 7 · 112 · 37 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7- 11+ 0 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-6,171] |
[a1,a2,a3,a4,a6] |
Generators |
[3:12:1] |
Generators of the group modulo torsion |
j |
-24137569/12692295 |
j-invariant |
L |
4.080809794764 |
L(r)(E,1)/r! |
Ω |
1.8204634171125 |
Real period |
R |
1.1208162043795 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128205bi1 |
Quadratic twists by: -3 |