Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
54720bb |
Isogeny class |
Conductor |
54720 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
236544 |
Modular degree for the optimal curve |
Δ |
-185904975052800 = -1 · 229 · 36 · 52 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -5 -4 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27468,-1870992] |
[a1,a2,a3,a4,a6] |
Generators |
[334:-5120:1] [244:2440:1] |
Generators of the group modulo torsion |
j |
-11993263569/972800 |
j-invariant |
L |
7.9254293350047 |
L(r)(E,1)/r! |
Ω |
0.18456529718712 |
Real period |
R |
5.3676323879651 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999957 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
54720ef1 1710k1 6080h1 |
Quadratic twists by: -4 8 -3 |