Atkin-Lehner |
2+ 3+ 5+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
87120d |
Isogeny class |
Conductor |
87120 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-1581228000000 = -1 · 28 · 33 · 56 · 114 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -1 11- -6 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1452,-56628] |
[a1,a2,a3,a4,a6] |
Generators |
[33:165:1] [121:1375:1] |
Generators of the group modulo torsion |
j |
3345408/15625 |
j-invariant |
L |
9.72550324395 |
L(r)(E,1)/r! |
Ω |
0.42621667735729 |
Real period |
R |
1.9015178117076 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000256 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
43560bi1 87120l1 87120b1 |
Quadratic twists by: -4 -3 -11 |