Atkin-Lehner |
3- 7+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
112749n |
Isogeny class |
Conductor |
112749 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
671328 |
Modular degree for the optimal curve |
Δ |
544745833216767 = 36 · 78 · 133 · 59 |
Discriminant |
Eigenvalues |
1 3- -4 7+ 4 13- 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-55788,-4950473] |
[a1,a2,a3,a4,a6] |
Generators |
[-139:420:1] |
Generators of the group modulo torsion |
j |
3330815508601/94495167 |
j-invariant |
L |
8.013256107934 |
L(r)(E,1)/r! |
Ω |
0.31118466758109 |
Real period |
R |
1.4306003596785 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999442308 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
112749e1 |
Quadratic twists by: -7 |