Properties

Label 1050.q
Number of curves $4$
Conductor $1050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1050.q1 1050p3 [1, 0, 0, -9338, 346542] [2] 1536  
1050.q2 1050p2 [1, 0, 0, -588, 5292] [2, 2] 768  
1050.q3 1050p1 [1, 0, 0, -88, -208] [2] 384 \(\Gamma_0(N)\)-optimal
1050.q4 1050p4 [1, 0, 0, 162, 18042] [2] 1536  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1050.q do not have complex multiplication.

Modular form 1050.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} + 2q^{13} + q^{14} + q^{16} + 6q^{17} + q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.