Atkin-Lehner |
3+ 5- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
8415h |
Isogeny class |
Conductor |
8415 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1600 |
Modular degree for the optimal curve |
Δ |
-15778125 = -1 · 33 · 55 · 11 · 17 |
Discriminant |
Eigenvalues |
1 3+ 5- 3 11- 3 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,51,118] |
[a1,a2,a3,a4,a6] |
Generators |
[2:14:1] |
Generators of the group modulo torsion |
j |
537367797/584375 |
j-invariant |
L |
6.0276529589397 |
L(r)(E,1)/r! |
Ω |
1.4643334843897 |
Real period |
R |
0.41163116347448 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8415c1 42075n1 92565t1 |
Quadratic twists by: -3 5 -11 |