Properties

Label 950.b
Number of curves $2$
Conductor $950$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("950.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 950.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
950.b1 950a2 [1, 0, 1, -1751, -31352] [] 800  
950.b2 950a1 [1, 0, 1, -1, 148] [] 160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 950.b have rank \(1\).

Modular form 950.2.a.b

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.