Atkin-Lehner |
3- 5+ 7+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615j |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-626913893908575 = -1 · 39 · 52 · 78 · 13 · 17 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 0 13- 17+ 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,20767,-357744] |
[a1,a2,a3,a4,a6] |
Generators |
[1106:36522:1] |
Generators of the group modulo torsion |
j |
1358742243975479/859964189175 |
j-invariant |
L |
3.5218567503003 |
L(r)(E,1)/r! |
Ω |
0.29490068243888 |
Real period |
R |
5.9712590715137 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999667 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205g1 |
Quadratic twists by: -3 |