Atkin-Lehner |
2+ 3- 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078k |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
188160 |
Modular degree for the optimal curve |
Δ |
-1238217831086391936 = -1 · 27 · 37 · 117 · 613 |
Discriminant |
Eigenvalues |
2+ 3- 1 2 11- -3 -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,45936,-53414528] |
[a1,a2,a3,a4,a6] |
Generators |
[413:5783:1] |
Generators of the group modulo torsion |
j |
14704504384534271/1698515543328384 |
j-invariant |
L |
3.8124698188054 |
L(r)(E,1)/r! |
Ω |
0.12925550333234 |
Real period |
R |
1.0534146158234 |
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 |
96624bf1 4026f1 |
Quadratic twists by: -4 -3 |