Atkin-Lehner |
2+ 3- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
48576bp |
Isogeny class |
Conductor |
48576 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-777216 = -1 · 210 · 3 · 11 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -3 3 11- 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,23,-1] |
[a1,a2,a3,a4,a6] |
Generators |
[58:447:1] |
Generators of the group modulo torsion |
j |
1257728/759 |
j-invariant |
L |
6.7670755689367 |
L(r)(E,1)/r! |
Ω |
1.6488295269241 |
Real period |
R |
4.1041693264209 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000056 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48576ck1 3036c1 |
Quadratic twists by: -4 8 |