Atkin-Lehner |
5- 13+ 101+ |
Signs for the Atkin-Lehner involutions |
Class |
85345d |
Isogeny class |
Conductor |
85345 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
3306240 |
Modular degree for the optimal curve |
Δ |
338051556574915625 = 55 · 139 · 1012 |
Discriminant |
Eigenvalues |
-1 0 5- 0 -4 13+ -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-24167032,-45722041686] |
[a1,a2,a3,a4,a6] |
Generators |
[-2838:1511:1] [10852:979421:1] |
Generators of the group modulo torsion |
j |
323395172637059952729/70036240625 |
j-invariant |
L |
6.688666426303 |
L(r)(E,1)/r! |
Ω |
0.068091630290573 |
Real period |
R |
19.646075142669 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998892 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6565c1 |
Quadratic twists by: 13 |