Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("19600.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bi1 19600dh2 [0, -1, 0, -163137088, -801950801728] [] 795648  
19600.bi2 19600dh1 [0, -1, 0, -6288, 211072] [] 21504 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 19600.2.a.bi

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

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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.