Atkin-Lehner |
3- 5+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
12675bd |
Isogeny class |
Conductor |
12675 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
134784 |
Modular degree for the optimal curve |
Δ |
-559221646623046875 = -1 · 33 · 59 · 139 |
Discriminant |
Eigenvalues |
0 3- 5+ -3 -3 13- 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,146467,28841219] |
[a1,a2,a3,a4,a6] |
Generators |
[-113:3295:1] |
Generators of the group modulo torsion |
j |
2097152/3375 |
j-invariant |
L |
3.829459809691 |
L(r)(E,1)/r! |
Ω |
0.19884111782084 |
Real period |
R |
1.6049077489854 |
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 |
38025bx1 2535c1 12675bc1 |
Quadratic twists by: -3 5 13 |