Atkin-Lehner |
3- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
117117z |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
78653952 |
Modular degree for the optimal curve |
Δ |
1.5284391783731E+26 |
Discriminant |
Eigenvalues |
-1 3- 0 7+ 11+ 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-4588557395,119635801234850] |
[a1,a2,a3,a4,a6] |
Generators |
[10875129180:-2024912449025:438976] |
Generators of the group modulo torsion |
j |
1382084250541230782125/19771083137421 |
j-invariant |
L |
2.9977760596855 |
L(r)(E,1)/r! |
Ω |
0.05273293473173 |
Real period |
R |
14.212066875078 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000266797 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39039w1 117117ca1 |
Quadratic twists by: -3 13 |