Atkin-Lehner |
2+ 3- 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360bp |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
10187596800 = 210 · 34 · 52 · 173 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 0 -2 17+ 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-11520,472068] |
[a1,a2,a3,a4,a6] |
Generators |
[66:-60:1] |
Generators of the group modulo torsion |
j |
33610279748/2025 |
j-invariant |
L |
7.7968267542149 |
L(r)(E,1)/r! |
Ω |
1.2192971069869 |
Real period |
R |
0.39965785972105 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999175 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34680j1 69360d1 |
Quadratic twists by: -4 17 |