Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744p |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1128960 |
Modular degree for the optimal curve |
Δ |
-3.3811606258123E+20 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 11- 0 -3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-743633,-918227967] |
[a1,a2,a3,a4,a6] |
Generators |
[4144:259127:1] |
Generators of the group modulo torsion |
j |
-226591821421000000/1684650343696353 |
j-invariant |
L |
4.7191600266823 |
L(r)(E,1)/r! |
Ω |
0.071903369572973 |
Real period |
R |
6.56319732257 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000066 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bg1 103488hi1 51744bb1 |
Quadratic twists by: -4 8 -7 |