Atkin-Lehner |
2- 3+ 11- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
52998m |
Isogeny class |
Conductor |
52998 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
192000 |
Modular degree for the optimal curve |
Δ |
4370115019776 = 210 · 3 · 117 · 73 |
Discriminant |
Eigenvalues |
2- 3+ 2 4 11- 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-4782,76011] |
[a1,a2,a3,a4,a6] |
Generators |
[-55:447:1] |
Generators of the group modulo torsion |
j |
6826561273/2466816 |
j-invariant |
L |
11.268730843078 |
L(r)(E,1)/r! |
Ω |
0.71130995553113 |
Real period |
R |
3.1684445734142 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999892 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4818a1 |
Quadratic twists by: -11 |