Atkin-Lehner |
2+ 13- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
27872b |
Isogeny class |
Conductor |
27872 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24384 |
Modular degree for the optimal curve |
Δ |
-29878784 = -1 · 29 · 13 · 672 |
Discriminant |
Eigenvalues |
2+ -3 -1 -1 0 13- 1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5203,144454] |
[a1,a2,a3,a4,a6] |
Generators |
[-38:536:1] [29:134:1] |
Generators of the group modulo torsion |
j |
-30423924092232/58357 |
j-invariant |
L |
4.9653659873888 |
L(r)(E,1)/r! |
Ω |
1.7957465350535 |
Real period |
R |
0.69126765532666 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27872d1 55744e1 |
Quadratic twists by: -4 8 |