Atkin-Lehner |
3- 11+ 17- 31- |
Signs for the Atkin-Lehner involutions |
Class |
52173l |
Isogeny class |
Conductor |
52173 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-340747654203 = -1 · 38 · 11 · 173 · 312 |
Discriminant |
Eigenvalues |
-2 3- 0 -1 11+ 0 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1065,31108] |
[a1,a2,a3,a4,a6] |
Generators |
[-41:76:1] [13:-140:1] |
Generators of the group modulo torsion |
j |
-183250432000/467417907 |
j-invariant |
L |
5.0122054375749 |
L(r)(E,1)/r! |
Ω |
0.84901933600977 |
Real period |
R |
0.49196027551962 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999934 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17391c1 |
Quadratic twists by: -3 |