Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("19600.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bc1 19600cm1 [0, -1, 0, -1220508, 519712012] [] 290304 \(\Gamma_0(N)\)-optimal
19600.bc2 19600cm2 [0, -1, 0, 1180492, 2205214012] [] 870912  

Rank

sage: E.rank()
 

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

Modular form 19600.2.a.bc

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{9} - 6q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.