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Properties

Label 249090l
Number of curves $2$
Conductor $249090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 249090l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.l2 249090l1 \([1, 1, 0, -417323, -103856823]\) \(170852246895169/159286500\) \(7493773723906500\) \([2]\) \(3317760\) \(1.9688\) \(\Gamma_0(N)\)-optimal
249090.l1 249090l2 \([1, 1, 0, -514793, -51827337]\) \(320701745122849/161130093750\) \(7580507216081343750\) \([2]\) \(6635520\) \(2.3154\)  

Rank

sage: E.rank()
 

The elliptic curves in class 249090l have rank \(1\).

Complex multiplication

The elliptic curves in class 249090l do not have complex multiplication.

Modular form 249090.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} - 2 q^{13} - 4 q^{14} + q^{15} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.