Atkin-Lehner |
3+ 5+ 29+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
69165a |
Isogeny class |
Conductor |
69165 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2649600 |
Modular degree for the optimal curve |
Δ |
-829883141982421875 = -1 · 39 · 510 · 29 · 533 |
Discriminant |
Eigenvalues |
2 3+ 5+ 1 0 -1 -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-12594663,-17203996681] |
[a1,a2,a3,a4,a6] |
j |
-11225147951993946697728/42162431640625 |
j-invariant |
L |
4.3275946516944 |
L(r)(E,1)/r! |
Ω |
0.040070321160834 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69165d1 |
Quadratic twists by: -3 |