Atkin-Lehner |
2+ 3+ 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078a |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
102400 |
Modular degree for the optimal curve |
Δ |
-103567668849672192 = -1 · 232 · 33 · 114 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 11+ -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-9717,15490357] |
[a1,a2,a3,a4,a6] |
Generators |
[-187:3371:1] |
Generators of the group modulo torsion |
j |
-3758215647796875/3835839587024896 |
j-invariant |
L |
2.9798216687524 |
L(r)(E,1)/r! |
Ω |
0.27071917667086 |
Real period |
R |
5.5035289804669 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
96624y1 12078q1 |
Quadratic twists by: -4 -3 |