Atkin-Lehner |
3+ 7- 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
9471b |
Isogeny class |
Conductor |
9471 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1728 |
Modular degree for the optimal curve |
Δ |
-5104869 = -1 · 3 · 73 · 112 · 41 |
Discriminant |
Eigenvalues |
1 3+ 3 7- 11- 1 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,39,-42] |
[a1,a2,a3,a4,a6] |
Generators |
[2:6:1] |
Generators of the group modulo torsion |
j |
6300872423/5104869 |
j-invariant |
L |
5.6217493604665 |
L(r)(E,1)/r! |
Ω |
1.3443479088771 |
Real period |
R |
0.69696112186243 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28413g1 66297p1 104181f1 |
Quadratic twists by: -3 -7 -11 |