Properties

Label 156.a
Number of curves $2$
Conductor $156$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 156.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156.a1 156a2 [0, -1, 0, -20, -24] [2] 24  
156.a2 156a1 [0, -1, 0, -5, 6] [2] 12 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 156.a have rank \(1\).

Complex multiplication

The elliptic curves in class 156.a do not have complex multiplication.

Modular form 156.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{5} - 2q^{7} + q^{9} - 4q^{11} + q^{13} + 4q^{15} + 2q^{17} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.