Atkin-Lehner |
2- 5+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
78650by |
Isogeny class |
Conductor |
78650 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
2688000 |
Modular degree for the optimal curve |
Δ |
287878662500000000 = 28 · 511 · 116 · 13 |
Discriminant |
Eigenvalues |
2- -2 5+ -4 11- 13+ 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-2544088,1561449792] |
[a1,a2,a3,a4,a6] |
Generators |
[872:2064:1] |
Generators of the group modulo torsion |
j |
65787589563409/10400000 |
j-invariant |
L |
3.9836356857796 |
L(r)(E,1)/r! |
Ω |
0.29794289892436 |
Real period |
R |
0.83565418419284 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000009019 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15730i1 650e1 |
Quadratic twists by: 5 -11 |