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Properties

Label 350727l
Number of curves $2$
Conductor $350727$
CM no
Rank $1$
Graph

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

Elliptic curves in class 350727l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350727.l2 350727l1 \([1, 0, 1, -66363326, -198690589645]\) \(218343927643978515625/11157852754782513\) \(1651762651885328313609057\) \([2]\) \(48660480\) \(3.4050\) \(\Gamma_0(N)\)-optimal
350727.l1 350727l2 \([1, 0, 1, -1048433311, -13066557189103]\) \(860952374874756362733625/2432265430303917\) \(360062575259007893277213\) \([2]\) \(97320960\) \(3.7516\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350727l have rank \(1\).

Complex multiplication

The elliptic curves in class 350727l do not have complex multiplication.

Modular form 350727.2.a.l

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