Properties

Label 193600fa
Number of curves 4
Conductor 193600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("193600.ix1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.ix4 193600fa1 [0, -1, 0, -548533, 153346437] [2] 3317760 \(\Gamma_0(N)\)-optimal
193600.ix3 193600fa2 [0, -1, 0, -1214033, -290542063] [2] 6635520  
193600.ix2 193600fa3 [0, -1, 0, -5388533, -4751993563] [2] 9953280  
193600.ix1 193600fa4 [0, -1, 0, -85914033, -306481042063] [2] 19906560  

Rank

sage: E.rank()
 

The elliptic curves in class 193600fa have rank \(1\).

Modular form 193600.2.a.ix

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.