Atkin-Lehner |
2- 3- 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
129360gj |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
1866240 |
Modular degree for the optimal curve |
Δ |
-903728726208000000 = -1 · 212 · 39 · 56 · 72 · 114 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 11- 1 6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,235499,12610499] |
[a1,a2,a3,a4,a6] |
Generators |
[374:12375:1] |
Generators of the group modulo torsion |
j |
7196694080651264/4502793796875 |
j-invariant |
L |
8.6029253609 |
L(r)(E,1)/r! |
Ω |
0.17356943616649 |
Real period |
R |
0.68839927531069 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000032125 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8085c1 129360eq1 |
Quadratic twists by: -4 -7 |