Atkin-Lehner |
2- 3- 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112cg |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-39049217703936 = -1 · 222 · 39 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3- 1 3 11- 4 -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8427,-423142] |
[a1,a2,a3,a4,a6] |
Generators |
[1589:63232:1] |
Generators of the group modulo torsion |
j |
-22164361129/13077504 |
j-invariant |
L |
8.318830850249 |
L(r)(E,1)/r! |
Ω |
0.24257714776663 |
Real period |
R |
4.286693391504 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000192 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8514g1 22704v1 |
Quadratic twists by: -4 -3 |