Properties

Label 24640bt
Number of curves 4
Conductor 24640
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("24640.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24640bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24640.l3 24640bt1 [0, 1, 0, -3585, -1609217] [2] 110592 \(\Gamma_0(N)\)-optimal
24640.l2 24640bt2 [0, 1, 0, -228865, -41844225] [2] 221184  
24640.l4 24640bt3 [0, 1, 0, 32255, 43326975] [2] 331776  
24640.l1 24640bt4 [0, 1, 0, -1671425, 807597823] [2] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 24640bt have rank \(1\).

Modular form 24640.2.a.l

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} - q^{7} + q^{9} - q^{11} + 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.