Properties

Label 244800et
Number of curves $2$
Conductor $244800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("et1")
 
E.isogeny_class()
 

Elliptic curves in class 244800et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244800.et1 244800et1 \([0, 0, 0, -36300, 1690000]\) \(1771561/612\) \(1827422208000000\) \([2]\) \(983040\) \(1.6302\) \(\Gamma_0(N)\)-optimal
244800.et2 244800et2 \([0, 0, 0, 107700, 11770000]\) \(46268279/46818\) \(-139797798912000000\) \([2]\) \(1966080\) \(1.9768\)  

Rank

sage: E.rank()
 

The elliptic curves in class 244800et have rank \(1\).

Complex multiplication

The elliptic curves in class 244800et do not have complex multiplication.

Modular form 244800.2.a.et

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - 6 q^{13} - q^{17} + 4 q^{19} + O(q^{20})\) 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.