Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("42320.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 42320z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42320.ba3 42320z1 [0, -1, 0, -705, 5192] [2] 23760 \(\Gamma_0(N)\)-optimal
42320.ba4 42320z2 [0, -1, 0, 1940, 32700] [2] 47520  
42320.ba1 42320z3 [0, -1, 0, -21865, -1236900] [2] 71280  
42320.ba2 42320z4 [0, -1, 0, -19220, -1550068] [2] 142560  

Rank

sage: E.rank()
 

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

Modular form 42320.2.a.ba

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} + 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 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.