Atkin-Lehner |
2- 3- 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048cy |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
350 |
Product of Tamagawa factors cp |
deg |
638400 |
Modular degree for the optimal curve |
Δ |
-107260371570223872 = -1 · 28 · 35 · 77 · 115 · 13 |
Discriminant |
Eigenvalues |
2- 3- 0 7- 11- 13+ -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-500893,137187479] |
[a1,a2,a3,a4,a6] |
Generators |
[2315:106722:1] |
Generators of the group modulo torsion |
j |
-54289957440781312000/418985826446187 |
j-invariant |
L |
7.9210662621413 |
L(r)(E,1)/r! |
Ω |
0.33623639090224 |
Real period |
R |
0.067308651009012 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000028 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12012a1 |
Quadratic twists by: -4 |