Atkin-Lehner |
3+ 7- 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
112749g |
Isogeny class |
Conductor |
112749 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3483648 |
Modular degree for the optimal curve |
Δ |
-3347151861783766491 = -1 · 312 · 77 · 133 · 592 |
Discriminant |
Eigenvalues |
-2 3+ 1 7- 4 13+ 6 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-536370,175132460] |
[a1,a2,a3,a4,a6] |
Generators |
[-345:17860:1] |
Generators of the group modulo torsion |
j |
-145054003223425024/28450321394859 |
j-invariant |
L |
3.2291166158148 |
L(r)(E,1)/r! |
Ω |
0.24080139044991 |
Real period |
R |
1.6762344138879 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999849528 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16107g1 |
Quadratic twists by: -7 |