Properties

Label 1050.k
Number of curves 8
Conductor 1050
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1050.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1050.k1 1050k7 [1, 1, 1, -8780813, -10018641469] [2] 27648  
1050.k2 1050k6 [1, 1, 1, -548813, -156705469] [2, 2] 13824  
1050.k3 1050k8 [1, 1, 1, -508813, -180465469] [2] 27648  
1050.k4 1050k4 [1, 1, 1, -108938, -13641469] [2] 9216  
1050.k5 1050k3 [1, 1, 1, -36813, -2081469] [4] 6912  
1050.k6 1050k2 [1, 1, 1, -14438, 344531] [2, 2] 4608  
1050.k7 1050k1 [1, 1, 1, -12438, 528531] [4] 2304 \(\Gamma_0(N)\)-optimal
1050.k8 1050k5 [1, 1, 1, 48062, 2594531] [2] 9216  

Rank

sage: E.rank()
 

The elliptic curves in class 1050.k have rank \(0\).

Modular form 1050.2.a.k

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - q^{12} - 2q^{13} - q^{14} + q^{16} + 6q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.