Atkin-Lehner |
2+ 3- 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
60840m |
Isogeny class |
Conductor |
60840 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-89946586080000 = -1 · 28 · 39 · 54 · 134 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -3 -2 13+ 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2028,457652] |
[a1,a2,a3,a4,a6] |
Generators |
[676:17550:1] [26:-650:1] |
Generators of the group modulo torsion |
j |
-173056/16875 |
j-invariant |
L |
8.8863352526827 |
L(r)(E,1)/r! |
Ω |
0.49619340866013 |
Real period |
R |
0.18655224071867 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
121680s1 20280u1 60840bv1 |
Quadratic twists by: -4 -3 13 |