Atkin-Lehner |
3+ 5- 29- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
48285b |
Isogeny class |
Conductor |
48285 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
-604562138319375 = -1 · 33 · 54 · 294 · 373 |
Discriminant |
Eigenvalues |
1 3+ 5- 4 0 2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-17859,1502240] |
[a1,a2,a3,a4,a6] |
Generators |
[-442:12401:8] |
Generators of the group modulo torsion |
j |
-23331627739527723/22391190308125 |
j-invariant |
L |
9.0368726901973 |
L(r)(E,1)/r! |
Ω |
0.46959033340621 |
Real period |
R |
2.4055203140228 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999976 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48285a1 |
Quadratic twists by: -3 |