Atkin-Lehner |
3+ 5+ 13+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
51675f |
Isogeny class |
Conductor |
51675 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
5661047925 = 32 · 52 · 132 · 533 |
Discriminant |
Eigenvalues |
-2 3+ 5+ -3 -5 13+ 1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-848,-8512] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:19:1] [-17:26:1] |
Generators of the group modulo torsion |
j |
2700743249920/226441917 |
j-invariant |
L |
3.6287106316631 |
L(r)(E,1)/r! |
Ω |
0.88934218191706 |
Real period |
R |
0.34001822784003 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999922 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51675bd1 |
Quadratic twists by: 5 |