Atkin-Lehner |
2+ 3- 5- 13- 41- |
Signs for the Atkin-Lehner involutions |
Class |
47970u |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
177408 |
Modular degree for the optimal curve |
Δ |
-2761766016750 = -1 · 2 · 313 · 53 · 132 · 41 |
Discriminant |
Eigenvalues |
2+ 3- 5- 1 6 13- 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-64584,6334038] |
[a1,a2,a3,a4,a6] |
Generators |
[117:-666:1] |
Generators of the group modulo torsion |
j |
-40867190734750849/3788430750 |
j-invariant |
L |
5.8050183333499 |
L(r)(E,1)/r! |
Ω |
0.7718602117335 |
Real period |
R |
0.31336731731091 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999844 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15990s1 |
Quadratic twists by: -3 |