Atkin-Lehner |
2- 3- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
21312bo |
Isogeny class |
Conductor |
21312 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-27592731648 = -1 · 210 · 39 · 372 |
Discriminant |
Eigenvalues |
2- 3- 0 0 0 6 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-120,-8008] |
[a1,a2,a3,a4,a6] |
Generators |
[97:945:1] |
Generators of the group modulo torsion |
j |
-256000/36963 |
j-invariant |
L |
5.8551976063526 |
L(r)(E,1)/r! |
Ω |
0.5264257706032 |
Real period |
R |
2.7806378094121 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
21312i1 5328d1 7104l1 |
Quadratic twists by: -4 8 -3 |