Atkin-Lehner |
2+ 5- 7- 61- |
Signs for the Atkin-Lehner involutions |
Class |
34160k |
Isogeny class |
Conductor |
34160 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
177408 |
Modular degree for the optimal curve |
Δ |
-1148254240000000 = -1 · 211 · 57 · 76 · 61 |
Discriminant |
Eigenvalues |
2+ -2 5- 7- -4 1 -7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,24320,734100] |
[a1,a2,a3,a4,a6] |
Generators |
[190:3500:1] [-10:700:1] |
Generators of the group modulo torsion |
j |
776723802140158/560671015625 |
j-invariant |
L |
6.6780887515933 |
L(r)(E,1)/r! |
Ω |
0.31037580033269 |
Real period |
R |
0.12807225383125 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17080j1 |
Quadratic twists by: -4 |