Properties

Label 350658.z
Number of curves $2$
Conductor $350658$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 350658.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.z1 350658z2 \([1, -1, 0, -165953277, -821067141317]\) \(391379047744832043625/964051690355138\) \(1245041878553966961574722\) \([2]\) \(66355200\) \(3.5014\)  
350658.z2 350658z1 \([1, -1, 0, -6512787, -22493503103]\) \(-23655968592999625/155579103523228\) \(-200925428845984009483932\) \([2]\) \(33177600\) \(3.1549\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350658.z have rank \(0\).

Complex multiplication

The elliptic curves in class 350658.z do not have complex multiplication.

Modular form 350658.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + q^{14} + q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.