Atkin-Lehner |
3- 11+ 19+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
99693b |
Isogeny class |
Conductor |
99693 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73216 |
Modular degree for the optimal curve |
Δ |
266479389 = 37 · 112 · 19 · 53 |
Discriminant |
Eigenvalues |
-1 3- -3 -3 11+ -4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2084,37122] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:-198:1] [-10:243:1] |
Generators of the group modulo torsion |
j |
1372441819897/365541 |
j-invariant |
L |
4.6856087667694 |
L(r)(E,1)/r! |
Ω |
1.7025310259767 |
Real period |
R |
0.34401786921381 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000329 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33231b1 |
Quadratic twists by: -3 |