Atkin-Lehner |
3+ 13+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
72111b |
Isogeny class |
Conductor |
72111 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
266112 |
Modular degree for the optimal curve |
Δ |
-4102558297437951 = -1 · 33 · 13 · 438 |
Discriminant |
Eigenvalues |
1 3+ -2 0 -4 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-12981,3128400] |
[a1,a2,a3,a4,a6] |
Generators |
[2806:50369:8] [1588:62374:1] |
Generators of the group modulo torsion |
j |
-38272753/648999 |
j-invariant |
L |
8.860359798413 |
L(r)(E,1)/r! |
Ω |
0.37040043033708 |
Real period |
R |
23.921029979293 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999738 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1677b1 |
Quadratic twists by: -43 |