Atkin-Lehner |
2+ 5- 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69290i |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
1347840 |
Modular degree for the optimal curve |
Δ |
-5356419304691406250 = -1 · 2 · 59 · 138 · 412 |
Discriminant |
Eigenvalues |
2+ -2 5- -1 -3 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,136717,109649568] |
[a1,a2,a3,a4,a6] |
Generators |
[264:-12945:1] [302:85585:8] |
Generators of the group modulo torsion |
j |
346456744439/6566406250 |
j-invariant |
L |
5.6063483059151 |
L(r)(E,1)/r! |
Ω |
0.18018570491629 |
Real period |
R |
5.185713177164 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999807 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
69290r1 |
Quadratic twists by: 13 |