Properties

Label 1050.r
Number of curves 2
Conductor 1050
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1050.r1")
sage: E.isogeny_class()

Elliptic curves in class 1050.r

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1050.r1 1050o2 [1, 0, 0, -109388, -13934358] 1 3000  
1050.r2 1050o1 [1, 0, 0, 22, -2748] 5 600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

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

Modular form 1050.2.a.r

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

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.