Properties

Label 162240fz
Number of curves $2$
Conductor $162240$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162240fz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.eu2 162240fz1 \([0, 1, 0, 43039, -9524865]\) \(6967871/35100\) \(-44412697549209600\) \([2]\) \(1548288\) \(1.8766\) \(\Gamma_0(N)\)-optimal
162240.eu1 162240fz2 \([0, 1, 0, -497761, -121254145]\) \(10779215329/1232010\) \(1558885683977256960\) \([2]\) \(3096576\) \(2.2232\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162240fz have rank \(0\).

Complex multiplication

The elliptic curves in class 162240fz do not have complex multiplication.

Modular form 162240.2.a.fz

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2q^{7} + q^{9} + 4q^{11} - q^{15} + 8q^{17} - 6q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.