Properties

Label 162240hx
Number of curves $4$
Conductor $162240$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("hx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162240hx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.w3 162240hx1 \([0, -1, 0, -43996, -3537314]\) \(30488290624/195\) \(60238576320\) \([2]\) \(258048\) \(1.2531\) \(\Gamma_0(N)\)-optimal
162240.w2 162240hx2 \([0, -1, 0, -44841, -3393495]\) \(504358336/38025\) \(751777432473600\) \([2, 2]\) \(516096\) \(1.5997\)  
162240.w1 162240hx3 \([0, -1, 0, -146241, 17555745]\) \(2186875592/428415\) \(67760205913620480\) \([2]\) \(1032192\) \(1.9463\)  
162240.w4 162240hx4 \([0, -1, 0, 43039, -15151839]\) \(55742968/658125\) \(-104092259880960000\) \([2]\) \(1032192\) \(1.9463\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 162240.2.a.hx

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.