Properties

Label 19600bx
Number of curves 2
Conductor 19600
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19600.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.o2 19600bx1 [0, 1, 0, -408, 119188] [] 34560 \(\Gamma_0(N)\)-optimal
19600.o1 19600bx2 [0, 1, 0, -196408, 33439188] [] 103680  

Rank

sage: E.rank()
 

The elliptic curves in class 19600bx have rank \(2\).

Modular form 19600.2.a.o

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{9} - 3q^{11} - 5q^{13} - 6q^{17} + q^{19} + O(q^{20}) \)

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.