Atkin-Lehner |
2- 3+ 5+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
47970x |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
-275284863360000 = -1 · 210 · 39 · 54 · 13 · 412 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 4 -4 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-7238,834517] |
[a1,a2,a3,a4,a6] |
Generators |
[-37:1043:1] |
Generators of the group modulo torsion |
j |
-2130256518363/13985920000 |
j-invariant |
L |
9.2835160206358 |
L(r)(E,1)/r! |
Ω |
0.47359904206351 |
Real period |
R |
0.9801029136567 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47970d1 |
Quadratic twists by: -3 |