Atkin-Lehner |
2+ 5+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
47600d |
Isogeny class |
Conductor |
47600 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
494592 |
Modular degree for the optimal curve |
Δ |
-3217055196320000000 = -1 · 211 · 57 · 72 · 177 |
Discriminant |
Eigenvalues |
2+ -1 5+ 7+ -2 -1 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-163408,90017312] |
[a1,a2,a3,a4,a6] |
Generators |
[-518:5950:1] [196:-8092:1] |
Generators of the group modulo torsion |
j |
-15079826167058/100532974885 |
j-invariant |
L |
7.6167696156243 |
L(r)(E,1)/r! |
Ω |
0.21690756113473 |
Real period |
R |
0.31352928045617 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23800h1 9520a1 |
Quadratic twists by: -4 5 |