Atkin-Lehner |
5- 7- 13+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
19565g |
Isogeny class |
Conductor |
19565 |
Conductor |
∏ cp |
77 |
Product of Tamagawa factors cp |
deg |
293216 |
Modular degree for the optimal curve |
Δ |
22478541845703125 = 511 · 77 · 13 · 43 |
Discriminant |
Eigenvalues |
-2 -2 5- 7- 2 13+ -7 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-162170,-24133326] |
[a1,a2,a3,a4,a6] |
Generators |
[-254:857:1] [-219:962:1] |
Generators of the group modulo torsion |
j |
471669658893725003776/22478541845703125 |
j-invariant |
L |
3.2061542732686 |
L(r)(E,1)/r! |
Ω |
0.23860953885565 |
Real period |
R |
0.17450420207417 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
97825i1 |
Quadratic twists by: 5 |