Atkin-Lehner |
2+ 3- 5- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970bi |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-218114590320 = -1 · 24 · 34 · 5 · 116 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5- -4 11- 2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1213,-27832] |
[a1,a2,a3,a4,a6] |
Generators |
[87:682:1] |
Generators of the group modulo torsion |
j |
-111284641/123120 |
j-invariant |
L |
4.9842488263797 |
L(r)(E,1)/r! |
Ω |
0.38771630733744 |
Real period |
R |
1.6069251962575 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000594 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
570m1 |
Quadratic twists by: -11 |