Properties

Label 121.b
Number of curves 2
Conductor 121
CM -11
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("121.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 121.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121.b1 121b2 [0, -1, 1, -887, -10143] [] 44  
121.b2 121b1 [0, -1, 1, -7, 10] [] 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 121.b have rank \(1\).

Modular form 121.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{4} - 3q^{5} - 2q^{9} + 2q^{12} + 3q^{15} + 4q^{16} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.