Properties

Label 162240eu
Number of curves $2$
Conductor $162240$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 162240eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.gy2 162240eu1 \([0, 1, 0, 486495, -137986497]\) \(40254822716/49359375\) \(-15613838982144000000\) \([2]\) \(2580480\) \(2.3690\) \(\Gamma_0(N)\)-optimal
162240.gy1 162240eu2 \([0, 1, 0, -2893505, -1328422497]\) \(4234737878642/1247410125\) \(789185877513486336000\) \([2]\) \(5160960\) \(2.7156\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162240eu have rank \(1\).

Complex multiplication

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

Modular form 162240.2.a.eu

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2 q^{7} + q^{9} + 4 q^{11} + q^{15} + 2 q^{19} + O(q^{20})\) Copy content 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.