Atkin-Lehner |
2+ 3+ 5- 7+ |
Signs for the Atkin-Lehner involutions |
Class |
47040y |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-275417656786944000 = -1 · 219 · 36 · 53 · 78 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7+ -3 -5 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-101985,28224225] |
[a1,a2,a3,a4,a6] |
Generators |
[-408:1323:1] [425:-7840:1] |
Generators of the group modulo torsion |
j |
-77626969/182250 |
j-invariant |
L |
8.3426739488705 |
L(r)(E,1)/r! |
Ω |
0.27397294177088 |
Real period |
R |
0.42292669766276 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47040gp1 1470f1 47040cl1 |
Quadratic twists by: -4 8 -7 |