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Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1050.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.b1 1050d1 \([1, 1, 0, -4375, -113225]\) \(-14822892630025/42\) \(-26250\) \([]\) \(600\) \(0.50455\) \(\Gamma_0(N)\)-optimal
1050.b2 1050d2 \([1, 1, 0, 550, -343500]\) \(46969655/130691232\) \(-51051262500000\) \([]\) \(3000\) \(1.3093\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1050.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.