Atkin-Lehner |
2+ 3+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078d |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
Δ |
7724790787118513328 = 24 · 39 · 116 · 614 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -2 11- 6 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2788170,1787655428] |
[a1,a2,a3,a4,a6] |
j |
121784006411470644723/392460030844816 |
j-invariant |
L |
2.8216473090558 |
L(r)(E,1)/r! |
Ω |
0.23513727575465 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
96624t2 12078o2 |
Quadratic twists by: -4 -3 |