Properties

Label 147294.cp
Number of curves 2
Conductor 147294
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("147294.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 147294.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
147294.cp1 147294bg2 [1, -1, 1, -54914, -4925847] [2] 663552  
147294.cp2 147294bg1 [1, -1, 1, -1994, -141879] [2] 331776 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 147294.cp have rank \(1\).

Modular form 147294.2.a.cp

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} + q^{8} + 2q^{10} + 4q^{11} + q^{16} - 4q^{17} + 4q^{19} + O(q^{20}) \)

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 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.