Atkin-Lehner |
3+ 7- 17+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117453d |
Isogeny class |
Conductor |
117453 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
38735546903978337 = 34 · 78 · 17 · 474 |
Discriminant |
Eigenvalues |
-1 3+ -2 7- 0 2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-104959,-9078868] |
[a1,a2,a3,a4,a6] |
j |
1086913000972513/329246716113 |
j-invariant |
L |
0.54295144055927 |
L(r)(E,1)/r! |
Ω |
0.27147626695401 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16779j1 |
Quadratic twists by: -7 |