Atkin-Lehner |
2+ 3- 17+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
47328l |
Isogeny class |
Conductor |
47328 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
473088 |
Modular degree for the optimal curve |
Δ |
-31127732577939456 = -1 · 212 · 37 · 173 · 294 |
Discriminant |
Eigenvalues |
2+ 3- -3 -2 -1 7 17+ 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,37683,8020539] |
[a1,a2,a3,a4,a6] |
Generators |
[45:-3132:1] |
Generators of the group modulo torsion |
j |
1444736517166592/7599544086411 |
j-invariant |
L |
5.3939232418046 |
L(r)(E,1)/r! |
Ω |
0.26712502463555 |
Real period |
R |
0.36058043614868 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47328e1 94656bc1 |
Quadratic twists by: -4 8 |