Atkin-Lehner |
2+ 7+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
41272c |
Isogeny class |
Conductor |
41272 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
31744 |
Modular degree for the optimal curve |
Δ |
1757857024 = 28 · 7 · 114 · 67 |
Discriminant |
Eigenvalues |
2+ -1 -3 7+ 11- -5 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3332,75124] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:308:1] [5:242:1] |
Generators of the group modulo torsion |
j |
15985604319568/6866629 |
j-invariant |
L |
5.9663250623514 |
L(r)(E,1)/r! |
Ω |
1.4661683866141 |
Real period |
R |
0.50866642576865 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82544o1 |
Quadratic twists by: -4 |