Atkin-Lehner |
3- 7- 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
112749t |
Isogeny class |
Conductor |
112749 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
72192 |
Modular degree for the optimal curve |
Δ |
-13264807101 = -1 · 3 · 78 · 13 · 59 |
Discriminant |
Eigenvalues |
1 3- 1 7- 3 13- -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1398,-20975] |
[a1,a2,a3,a4,a6] |
Generators |
[62247:2957422:27] |
Generators of the group modulo torsion |
j |
-2565726409/112749 |
j-invariant |
L |
10.951666777368 |
L(r)(E,1)/r! |
Ω |
0.3894175177265 |
Real period |
R |
7.0308000430839 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999778409 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16107a1 |
Quadratic twists by: -7 |