Atkin-Lehner |
3+ 5- 11+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
12045a |
Isogeny class |
Conductor |
12045 |
Conductor |
∏ cp |
7 |
Product of Tamagawa factors cp |
deg |
3696 |
Modular degree for the optimal curve |
Δ |
188203125 = 3 · 57 · 11 · 73 |
Discriminant |
Eigenvalues |
0 3+ 5- 2 11+ 4 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-335,2381] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:62:1] |
Generators of the group modulo torsion |
j |
4170171252736/188203125 |
j-invariant |
L |
3.8641578186338 |
L(r)(E,1)/r! |
Ω |
1.7754809687739 |
Real period |
R |
0.31091436924853 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36135f1 60225o1 |
Quadratic twists by: -3 5 |