Atkin-Lehner |
2+ 3- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
81312u |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1672704 |
Modular degree for the optimal curve |
Δ |
983885779885510656 = 212 · 33 · 73 · 1110 |
Discriminant |
Eigenvalues |
2+ 3- 3 7+ 11- -4 -7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-429469,-97394101] |
[a1,a2,a3,a4,a6] |
Generators |
[-106645:852396:343] |
Generators of the group modulo torsion |
j |
82458112/9261 |
j-invariant |
L |
9.2957772653627 |
L(r)(E,1)/r! |
Ω |
0.18785669091912 |
Real period |
R |
8.2472240044891 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000915 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81312bi1 81312bw1 |
Quadratic twists by: -4 -11 |