Atkin-Lehner |
2- 3- 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
82908x |
Isogeny class |
Conductor |
82908 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1013760 |
Modular degree for the optimal curve |
Δ |
767955336465744 = 24 · 311 · 78 · 47 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 4 -4 -4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1679916,-838067335] |
[a1,a2,a3,a4,a6] |
Generators |
[-748:29:1] [1792:43659:1] |
Generators of the group modulo torsion |
j |
382076793536512/559629 |
j-invariant |
L |
9.8653119170747 |
L(r)(E,1)/r! |
Ω |
0.13261043547669 |
Real period |
R |
6.1994316170389 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997498 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27636k1 11844d1 |
Quadratic twists by: -3 -7 |