Atkin-Lehner |
2- 3+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
57408cj |
Isogeny class |
Conductor |
57408 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
393216 |
Modular degree for the optimal curve |
Δ |
-3536553011576832 = -1 · 218 · 38 · 132 · 233 |
Discriminant |
Eigenvalues |
2- 3+ 4 -2 -2 13+ 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6241,-2865407] |
[a1,a2,a3,a4,a6] |
Generators |
[957:29440:1] |
Generators of the group modulo torsion |
j |
-102568953241/13490879103 |
j-invariant |
L |
6.6002548384806 |
L(r)(E,1)/r! |
Ω |
0.19735670262729 |
Real period |
R |
2.7869397350666 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000115 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57408be1 14352bl1 |
Quadratic twists by: -4 8 |