Properties

Label 19600.bu
Number of curves $4$
Conductor $19600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19600.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bu1 19600cc3 [0, 0, 0, -5246675, -4625440750] [2] 442368  
19600.bu2 19600cc4 [0, 0, 0, -1718675, 810423250] [2] 442368  
19600.bu3 19600cc2 [0, 0, 0, -346675, -63540750] [2, 2] 221184  
19600.bu4 19600cc1 [0, 0, 0, 45325, -5916750] [2] 110592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19600.bu have rank \(1\).

Modular form 19600.2.a.bu

sage: E.q_eigenform(10)
 
\( q - 3q^{9} - 4q^{11} - 6q^{13} + 2q^{17} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.