Properties

Label 156090k
Number of curves $4$
Conductor $156090$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 156090k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156090.bi3 156090k1 [1, 0, 0, -8291, 289521] [2] 276480 \(\Gamma_0(N)\)-optimal
156090.bi2 156090k2 [1, 0, 0, -10711, 106085] [2, 2] 552960  
156090.bi4 156090k3 [1, 0, 0, 41319, 844911] [2] 1105920  
156090.bi1 156090k4 [1, 0, 0, -101461, -12362965] [2] 1105920  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 156090.2.a.k

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.