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Properties

Label 1050.d
Number of curves $2$
Conductor $1050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1050.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.d1 1050e1 \([1, 1, 0, -80, 0]\) \(461889917/263424\) \(32928000\) \([2]\) \(384\) \(0.13228\) \(\Gamma_0(N)\)-optimal
1050.d2 1050e2 \([1, 1, 0, 320, 400]\) \(28849701763/16941456\) \(-2117682000\) \([2]\) \(768\) \(0.47886\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1050.d have rank \(1\).

Complex multiplication

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

Modular form 1050.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{11} - q^{12} - 6 q^{13} - q^{14} + q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.