Atkin-Lehner |
2- 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144bv |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
3342062592 = 210 · 36 · 112 · 37 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 11+ -4 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-445,2461] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:77:1] [-7:72:1] |
Generators of the group modulo torsion |
j |
9538484224/3263733 |
j-invariant |
L |
7.0160183330348 |
L(r)(E,1)/r! |
Ω |
1.2987543271259 |
Real period |
R |
2.7010567688801 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000347 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144bn1 19536q1 |
Quadratic twists by: -4 8 |