Properties

Label 193600gh
Number of curves 2
Conductor 193600
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("193600.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bi2 193600gh1 [0, 1, 0, -513, 2143] [] 110592 \(\Gamma_0(N)\)-optimal
193600.bi1 193600gh2 [0, 1, 0, -35713, 2585823] [] 331776  

Rank

sage: E.rank()
 

The elliptic curves in class 193600gh have rank \(2\).

Modular form 193600.2.a.bi

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{7} + q^{9} + 4q^{13} - 6q^{17} + 2q^{19} + O(q^{20}) \)

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.