Atkin-Lehner |
2+ 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
19936c |
Isogeny class |
Conductor |
19936 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
-42888237056 = -1 · 212 · 76 · 89 |
Discriminant |
Eigenvalues |
2+ -3 -3 7- -6 -4 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-23404,1378144] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:1652:1] [2199:2989:27] |
Generators of the group modulo torsion |
j |
-346125847768128/10470761 |
j-invariant |
L |
3.8461504199769 |
L(r)(E,1)/r! |
Ω |
1.0636224307628 |
Real period |
R |
0.15067025935523 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19936g1 39872o1 |
Quadratic twists by: -4 8 |