Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744x |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-243449535909888 = -1 · 212 · 38 · 77 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 11- -2 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,14831,-288287] |
[a1,a2,a3,a4,a6] |
Generators |
[9316:142155:64] |
Generators of the group modulo torsion |
j |
748613312/505197 |
j-invariant |
L |
3.7740356777598 |
L(r)(E,1)/r! |
Ω |
0.31534892253158 |
Real period |
R |
5.9839045071781 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000005 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744cj2 103488dc1 7392g4 |
Quadratic twists by: -4 8 -7 |