Atkin-Lehner |
3+ 11- 103+ |
Signs for the Atkin-Lehner involutions |
Class |
112167d |
Isogeny class |
Conductor |
112167 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
54144 |
Modular degree for the optimal curve |
Δ |
-245309229 = -1 · 39 · 112 · 103 |
Discriminant |
Eigenvalues |
-1 3+ 3 -4 11- -2 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-56,784] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:32:1] [1:-28:1] |
Generators of the group modulo torsion |
j |
-8019/103 |
j-invariant |
L |
8.1588685201021 |
L(r)(E,1)/r! |
Ω |
1.4893864076634 |
Real period |
R |
2.7390032819682 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000329 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
112167c1 112167b1 |
Quadratic twists by: -3 -11 |