Properties

Label 159936.y
Number of curves $2$
Conductor $159936$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 159936.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159936.y1 159936il2 \([0, -1, 0, -1447968097, -6069944496671]\) \(222165413800219579417/118033833938006016\) \(178373673332152996735959957504\) \([]\) \(243855360\) \(4.3042\)  
159936.y2 159936il1 \([0, -1, 0, -834519457, 9279100581409]\) \(42531320912955257257/1127938881456\) \(1704550253659797653028864\) \([]\) \(81285120\) \(3.7549\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 159936.y have rank \(1\).

Complex multiplication

The elliptic curves in class 159936.y do not have complex multiplication.

Modular form 159936.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3q^{5} + q^{9} + 6q^{11} - 5q^{13} + 3q^{15} - q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

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.