Properties

Label 42320.l
Number of curves 4
Conductor 42320
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("42320.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 42320.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42320.l1 42320c4 [0, 0, 0, -56603, -5183142] [2] 98560  
42320.l2 42320c2 [0, 0, 0, -3703, -73002] [2, 2] 49280  
42320.l3 42320c1 [0, 0, 0, -1058, 12167] [2] 24640 \(\Gamma_0(N)\)-optimal
42320.l4 42320c3 [0, 0, 0, 6877, -413678] [2] 98560  

Rank

sage: E.rank()
 

The elliptic curves in class 42320.l have rank \(0\).

Modular form 42320.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.