Atkin-Lehner |
2+ 3- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
76608bx |
Isogeny class |
Conductor |
76608 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
85948890048 = 26 · 312 · 7 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 4 7+ -2 -6 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-30243,-2024300] |
[a1,a2,a3,a4,a6] |
Generators |
[5505870:-14498083:27000] |
Generators of the group modulo torsion |
j |
65567831132224/1842183 |
j-invariant |
L |
7.9996018229749 |
L(r)(E,1)/r! |
Ω |
0.36202959081723 |
Real period |
R |
11.048270674844 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995895 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
76608ci1 38304m2 25536bk1 |
Quadratic twists by: -4 8 -3 |