Properties

Label 158400eg
Number of curves 4
Conductor 158400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("158400.hj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 158400eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.hj3 158400eg1 [0, 0, 0, -11100, -434000] [2] 262144 \(\Gamma_0(N)\)-optimal
158400.hj2 158400eg2 [0, 0, 0, -29100, 1330000] [2, 2] 524288  
158400.hj1 158400eg3 [0, 0, 0, -425100, 106666000] [2] 1048576  
158400.hj4 158400eg4 [0, 0, 0, 78900, 8890000] [2] 1048576  

Rank

sage: E.rank()
 

The elliptic curves in class 158400eg have rank \(1\).

Modular form 158400.2.a.hj

sage: E.q_eigenform(10)
 
\( q - q^{11} + 2q^{13} + 6q^{17} + O(q^{20}) \)

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.