Properties

Label 48400cz
Number of curves 3
Conductor 48400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("48400.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48400cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.bd2 48400cz1 [0, -1, 0, -1356208, -608049088] [] 691200 \(\Gamma_0(N)\)-optimal
48400.bd3 48400cz2 [0, -1, 0, 9533792, 6376070912] [] 3456000  
48400.bd1 48400cz3 [0, -1, 0, -1467876208, 21646998590912] [] 17280000  

Rank

sage: E.rank()
 

The elliptic curves in class 48400cz have rank \(0\).

Modular form 48400.2.a.bd

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

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.