Properties

Label 19600.s
Number of curves 2
Conductor 19600
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19600.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.s1 19600bv2 [0, 1, 0, -143488, 20855988] [] 108864  
19600.s2 19600bv1 [0, 1, 0, -6288, -163052] [] 36288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 19600.2.a.s

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

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 LMFDB 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 LMFDB labels.