Properties

Label 19600cj
Number of curves 2
Conductor 19600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19600.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bd2 19600cj1 [0, -1, 0, -6533, -995063] [] 55296 \(\Gamma_0(N)\)-optimal
19600.bd1 19600cj2 [0, -1, 0, -986533, -376825063] [] 165888  

Rank

sage: E.rank()
 

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

Modular form 19600.2.a.bd

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.