Atkin-Lehner |
2- 3+ 5- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
4140b |
Isogeny class |
Conductor |
4140 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
2829431250000 = 24 · 39 · 58 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 -4 -2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5832,-151119] |
[a1,a2,a3,a4,a6] |
Generators |
[-48:135:1] |
Generators of the group modulo torsion |
j |
69657034752/8984375 |
j-invariant |
L |
3.5815586951676 |
L(r)(E,1)/r! |
Ω |
0.55095994314187 |
Real period |
R |
0.54171492558116 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16560bf1 66240f1 4140a1 20700c1 |
Quadratic twists by: -4 8 -3 5 |