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Properties

Label 156090by
Number of curves $2$
Conductor $156090$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 156090by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156090.e2 156090by1 [1, 1, 0, -1240978, 551258932] [2] 6451200 \(\Gamma_0(N)\)-optimal
156090.e1 156090by2 [1, 1, 0, -20058898, 34570294708] [2] 12902400  

Rank

sage: E.rank()
 

The elliptic curves in class 156090by have rank \(1\).

Complex multiplication

The elliptic curves in class 156090by do not have complex multiplication.

Modular form 156090.2.a.by

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - 4q^{13} - 4q^{14} + q^{15} + q^{16} - 4q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.