Atkin-Lehner |
2+ 3+ 11+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
12078b |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-539306856 = -1 · 23 · 33 · 11 · 613 |
Discriminant |
Eigenvalues |
2+ 3+ -3 2 11+ -1 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-411,3501] |
[a1,a2,a3,a4,a6] |
j |
-284760442539/19974328 |
j-invariant |
L |
1.0772441415607 |
L(r)(E,1)/r! |
Ω |
1.615866212341 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
96624bd1 12078r2 |
Quadratic twists by: -4 -3 |