Atkin-Lehner |
2- 3- 11+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
116688x |
Isogeny class |
Conductor |
116688 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
1247477271625728 = 218 · 34 · 112 · 134 · 17 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 11+ 13- 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-48328,3703412] |
[a1,a2,a3,a4,a6] |
Generators |
[-244:1014:1] [68:858:1] |
Generators of the group modulo torsion |
j |
3047678972871625/304559880768 |
j-invariant |
L |
13.6265392159 |
L(r)(E,1)/r! |
Ω |
0.47097152223075 |
Real period |
R |
0.9041509527317 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999118 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14586b1 |
Quadratic twists by: -4 |