Atkin-Lehner |
2+ 3- 7- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
98112y |
Isogeny class |
Conductor |
98112 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
683575345152 = 218 · 36 · 72 · 73 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- -2 -2 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4193,-98049] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:84:1] |
Generators of the group modulo torsion |
j |
31107273625/2607633 |
j-invariant |
L |
8.401085714412 |
L(r)(E,1)/r! |
Ω |
0.59644468963282 |
Real period |
R |
1.1737726701595 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003546 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
98112bd1 1533a1 |
Quadratic twists by: -4 8 |