Atkin-Lehner |
2+ 3+ 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
78144t |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
859584 = 26 · 3 · 112 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 11- -4 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-144,714] |
[a1,a2,a3,a4,a6] |
Generators |
[74:75:8] |
Generators of the group modulo torsion |
j |
5195695168/13431 |
j-invariant |
L |
4.4864749762059 |
L(r)(E,1)/r! |
Ω |
2.8204371904736 |
Real period |
R |
3.1814039277454 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999962996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144bg1 39072m2 |
Quadratic twists by: -4 8 |