Atkin-Lehner |
2- 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144bu |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50176 |
Modular degree for the optimal curve |
Δ |
-1080262656 = -1 · 215 · 34 · 11 · 37 |
Discriminant |
Eigenvalues |
2- 3+ -3 -4 11+ 0 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-577,5761] |
[a1,a2,a3,a4,a6] |
Generators |
[1:-72:1] [-8:99:1] |
Generators of the group modulo torsion |
j |
-649461896/32967 |
j-invariant |
L |
6.1470912954045 |
L(r)(E,1)/r! |
Ω |
1.5339497184918 |
Real period |
R |
0.5009202079209 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999799 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78144db1 39072r1 |
Quadratic twists by: -4 8 |