Properties

Label 142296h
Number of curves 4
Conductor 142296
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("142296.cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 142296h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142296.cs3 142296h1 [0, 1, 0, -73124, -7362720] [2] 737280 \(\Gamma_0(N)\)-optimal
142296.cs2 142296h2 [0, 1, 0, -191704, 22424576] [2, 2] 1474560  
142296.cs1 142296h3 [0, 1, 0, -2800464, 1802642400] [2] 2949120  
142296.cs4 142296h4 [0, 1, 0, 519776, 150490976] [2] 2949120  

Rank

sage: E.rank()
 

The elliptic curves in class 142296h have rank \(1\).

Modular form 142296.2.a.cs

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} + 2q^{13} - 2q^{15} + 6q^{17} + O(q^{20}) \)

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.