Atkin-Lehner |
3+ 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
3135b |
Isogeny class |
Conductor |
3135 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-112662495 = -1 · 34 · 5 · 114 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 11- -2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,120,120] |
[a1,a2,a3,a4,a6] |
Generators |
[24:120:1] |
Generators of the group modulo torsion |
j |
191003460479/112662495 |
j-invariant |
L |
1.9523265426857 |
L(r)(E,1)/r! |
Ω |
1.1393041678651 |
Real period |
R |
3.4272261925348 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
50160ca1 9405e1 15675s1 34485h1 |
Quadratic twists by: -4 -3 5 -11 |