Atkin-Lehner |
2+ 3+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078c |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3200 |
Modular degree for the optimal curve |
Δ |
-36234 = -1 · 2 · 33 · 11 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -2 11- 1 -4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-570,-5098] |
[a1,a2,a3,a4,a6] |
j |
-759299343867/1342 |
j-invariant |
L |
0.9770011739739 |
L(r)(E,1)/r! |
Ω |
0.48850058698695 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96624s1 12078n1 |
Quadratic twists by: -4 -3 |