Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ea1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162240ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.bl2 162240ea1 \([0, -1, 0, 43039, 9524865]\) \(6967871/35100\) \(-44412697549209600\) \([2]\) \(1548288\) \(1.8766\) \(\Gamma_0(N)\)-optimal
162240.bl1 162240ea2 \([0, -1, 0, -497761, 121254145]\) \(10779215329/1232010\) \(1558885683977256960\) \([2]\) \(3096576\) \(2.2232\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 162240.2.a.ea

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.