Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 162240.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.i1 162240dk1 \([0, -1, 0, -39364381, -84592286819]\) \(621217777580032/74733890625\) \(811535868185254992000000\) \([2]\) \(23482368\) \(3.3185\) \(\Gamma_0(N)\)-optimal
162240.i2 162240dk2 \([0, -1, 0, 56732399, -433250624015]\) \(116227003261808/533935546875\) \(-92768160515004000000000000\) \([2]\) \(46964736\) \(3.6651\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 162240.2.a.i

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