Properties

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

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Show commands: SageMath
E = EllipticCurve("eb1")
 
E.isogeny_class()
 

Elliptic curves in class 162240.eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.eb1 162240hl2 \([0, -1, 0, -372025, 76252825]\) \(131096512/18225\) \(791621636394700800\) \([2]\) \(3354624\) \(2.1609\)  
162240.eb2 162240hl1 \([0, -1, 0, -97400, -10473750]\) \(150568768/16875\) \(11452859322840000\) \([2]\) \(1677312\) \(1.8143\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 162240.2.a.eb

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 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.