Properties

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

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Show commands: SageMath
E = EllipticCurve("gp1")
 
E.isogeny_class()
 

Elliptic curves in class 162240gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.ga2 162240gp1 \([0, 1, 0, -576, 4590]\) \(150568768/16875\) \(2372760000\) \([2]\) \(129024\) \(0.53181\) \(\Gamma_0(N)\)-optimal
162240.ga1 162240gp2 \([0, 1, 0, -2201, -35385]\) \(131096512/18225\) \(164005171200\) \([2]\) \(258048\) \(0.87839\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 162240.2.a.gp

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