Atkin-Lehner |
2+ 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
39872g |
Isogeny class |
Conductor |
39872 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
-1227512373435170816 = -1 · 248 · 72 · 89 |
Discriminant |
Eigenvalues |
2+ 1 1 7+ -6 -4 -7 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1735265,-882018049] |
[a1,a2,a3,a4,a6] |
Generators |
[9629:935564:1] [247495:7340032:125] |
Generators of the group modulo torsion |
j |
-2204354621486221849/4682588094464 |
j-invariant |
L |
10.095936715147 |
L(r)(E,1)/r! |
Ω |
0.065761666109788 |
Real period |
R |
19.190391059838 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39872bj1 1246a1 |
Quadratic twists by: -4 8 |