Atkin-Lehner |
2+ 3+ 5- 29- |
Signs for the Atkin-Lehner involutions |
Class |
27840bf |
Isogeny class |
Conductor |
27840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-313200000000 = -1 · 210 · 33 · 58 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 3 -1 -1 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48865,-4141463] |
[a1,a2,a3,a4,a6] |
Generators |
[264:1135:1] |
Generators of the group modulo torsion |
j |
-12601619217266944/305859375 |
j-invariant |
L |
5.8585180987462 |
L(r)(E,1)/r! |
Ω |
0.16055310543616 |
Real period |
R |
4.5611996127629 |
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 |
27840el1 3480f1 83520bb1 |
Quadratic twists by: -4 8 -3 |