Atkin-Lehner |
2- 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
89376bp |
Isogeny class |
Conductor |
89376 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
83468046376512 = 26 · 35 · 710 · 19 |
Discriminant |
Eigenvalues |
2- 3+ -4 7- -4 -4 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-73810,7730416] |
[a1,a2,a3,a4,a6] |
Generators |
[138:392:1] |
Generators of the group modulo torsion |
j |
5906184342976/11085417 |
j-invariant |
L |
2.7183962641883 |
L(r)(E,1)/r! |
Ω |
0.60785841376213 |
Real period |
R |
2.2360439503187 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000024654 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
89376bc1 12768ba1 |
Quadratic twists by: -4 -7 |