Atkin-Lehner |
2+ 3+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384d |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
12495115033509888 = 224 · 34 · 13 · 294 |
Discriminant |
Eigenvalues |
2+ 3+ 2 4 4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-23004257,-42460197663] |
[a1,a2,a3,a4,a6] |
Generators |
[-5882158721498974794115223565742412397160:-4236692546675899740505334005019530957:2124290805587064587664563467837036625] |
Generators of the group modulo torsion |
j |
5135804003824189180057/47665081152 |
j-invariant |
L |
8.2481886625454 |
L(r)(E,1)/r! |
Ω |
0.068936225510048 |
Real period |
R |
59.824777176447 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001816 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384cv4 2262h3 |
Quadratic twists by: -4 8 |