Atkin-Lehner |
2+ 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144a |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
40960 |
Modular degree for the optimal curve |
Δ |
11842879488 = 218 · 3 · 11 · 372 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 11+ -4 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-833,-7359] |
[a1,a2,a3,a4,a6] |
Generators |
[-17:40:1] |
Generators of the group modulo torsion |
j |
244140625/45177 |
j-invariant |
L |
4.4685852307292 |
L(r)(E,1)/r! |
Ω |
0.89992860943062 |
Real period |
R |
2.4827442880566 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002874 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144cw1 1221c1 |
Quadratic twists by: -4 8 |