Atkin-Lehner |
7- 13+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
27391b |
Isogeny class |
Conductor |
27391 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
68992 |
Modular degree for the optimal curve |
Δ |
-925477877233 = -1 · 73 · 137 · 43 |
Discriminant |
Eigenvalues |
1 0 0 7- -3 13+ 0 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-197297,-33681726] |
[a1,a2,a3,a4,a6] |
Generators |
[3269937339578:-431455455201849:189119224] |
Generators of the group modulo torsion |
j |
-2476237379914317375/2698186231 |
j-invariant |
L |
5.0918368774736 |
L(r)(E,1)/r! |
Ω |
0.11326332506331 |
Real period |
R |
22.477871255447 |
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 |
27391f2 |
Quadratic twists by: -7 |