Atkin-Lehner |
2- 43- |
Signs for the Atkin-Lehner involutions |
Class |
172a |
Isogeny class |
Conductor |
172 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
12 |
Modular degree for the optimal curve |
Δ |
-11008 = -1 · 28 · 43 |
Discriminant |
Eigenvalues |
2- -2 0 -4 -3 -1 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-13,15] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:6:1] |
Generators of the group modulo torsion |
j |
-1024000/43 |
j-invariant |
L |
1.0159589214554 |
L(r)(E,1)/r! |
Ω |
4.0096273259976 |
Real period |
R |
0.76013966300667 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
688b1 2752b1 1548c1 4300b1 |
Quadratic twists by: -4 8 -3 5 |