Properties

Label 19600bw
Number of curves 2
Conductor 19600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19600.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.p2 19600bw1 [0, 1, 0, 322992, -93020012] [] 338688 \(\Gamma_0(N)\)-optimal
19600.p1 19600bw2 [0, 1, 0, -3107008, 3659399988] [] 1016064  

Rank

sage: E.rank()
 

The elliptic curves in class 19600bw have rank \(0\).

Modular form 19600.2.a.p

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

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.