Atkin-Lehner |
2+ 3+ 5- 11- |
Signs for the Atkin-Lehner involutions |
Class |
54450z |
Isogeny class |
Conductor |
54450 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
768000 |
Modular degree for the optimal curve |
Δ |
-180865305843750000 = -1 · 24 · 33 · 59 · 118 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -4 11- 0 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,53883,19873541] |
[a1,a2,a3,a4,a6] |
Generators |
[169:5728:1] |
Generators of the group modulo torsion |
j |
185193/1936 |
j-invariant |
L |
3.0439070341874 |
L(r)(E,1)/r! |
Ω |
0.23558486748174 |
Real period |
R |
3.2301597580434 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000044 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
54450es1 54450er1 4950bc1 |
Quadratic twists by: -3 5 -11 |