Atkin-Lehner |
2- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712ck |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
1078272 |
Modular degree for the optimal curve |
Δ |
-1572370900499316736 = -1 · 214 · 76 · 138 |
Discriminant |
Eigenvalues |
2- 0 1 7- -2 13+ -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1573052,-761778992] |
[a1,a2,a3,a4,a6] |
Generators |
[2028:66248:1] |
Generators of the group modulo torsion |
j |
-32209663824/117649 |
j-invariant |
L |
5.8839059870054 |
L(r)(E,1)/r! |
Ω |
0.067388971829138 |
Real period |
R |
1.2126749269712 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993416 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712a1 18928u1 75712bq1 |
Quadratic twists by: -4 8 13 |