Atkin-Lehner |
3+ 7+ 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
112749a |
Isogeny class |
Conductor |
112749 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
397824 |
Modular degree for the optimal curve |
Δ |
-786855092424219 = -1 · 34 · 78 · 134 · 59 |
Discriminant |
Eigenvalues |
1 3+ -1 7+ 0 13+ -7 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-13598,-1486869] |
[a1,a2,a3,a4,a6] |
Generators |
[10046:1001879:1] |
Generators of the group modulo torsion |
j |
-48240789289/136493019 |
j-invariant |
L |
4.5552742496175 |
L(r)(E,1)/r! |
Ω |
0.20484568452365 |
Real period |
R |
5.5593974291466 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999165085 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
112749s1 |
Quadratic twists by: -7 |