Properties

Label 350727k
Number of curves $2$
Conductor $350727$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 350727k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350727.k2 350727k1 \([1, 1, 0, -138873, 19843560]\) \(2000852317801/2094417\) \(310048882531713\) \([2]\) \(3649536\) \(1.6979\) \(\Gamma_0(N)\)-optimal
350727.k1 350727k2 \([1, 1, 0, -173258, 9218595]\) \(3885442650361/1996623837\) \(295571984708886093\) \([2]\) \(7299072\) \(2.0445\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350727k have rank \(0\).

Complex multiplication

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

Modular form 350727.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + 4 q^{10} - 6 q^{11} + q^{12} - q^{13} - 2 q^{14} - 4 q^{15} - q^{16} - q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.