Atkin-Lehner |
3+ 11+ 17+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
72369c |
Isogeny class |
Conductor |
72369 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1013760 |
Modular degree for the optimal curve |
Δ |
-60880365742977 = -1 · 39 · 114 · 173 · 43 |
Discriminant |
Eigenvalues |
1 3+ 0 -4 11+ -3 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5245467,-4622758390] |
[a1,a2,a3,a4,a6] |
j |
-810932943631255171875/3093043019 |
j-invariant |
L |
0.19951864535229 |
L(r)(E,1)/r! |
Ω |
0.04987966353214 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72369h1 |
Quadratic twists by: -3 |