Properties

Label 350658ed
Number of curves $4$
Conductor $350658$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 350658ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.ed4 350658ed1 \([1, -1, 1, -652334, -330639955]\) \(-23771111713777/22848457968\) \(-29508051606714826992\) \([2]\) \(9830400\) \(2.4321\) \(\Gamma_0(N)\)-optimal
350658.ed3 350658ed2 \([1, -1, 1, -12173954, -16341083107]\) \(154502321244119857/55101928644\) \(71162375873849604036\) \([2, 2]\) \(19660800\) \(2.7787\)  
350658.ed2 350658ed3 \([1, -1, 1, -13927244, -11325271075]\) \(231331938231569617/90942310746882\) \(117449081356442569622658\) \([2]\) \(39321600\) \(3.1252\)  
350658.ed1 350658ed4 \([1, -1, 1, -194766584, -1046163516307]\) \(632678989847546725777/80515134\) \(103982716580742846\) \([2]\) \(39321600\) \(3.1252\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350658ed have rank \(1\).

Complex multiplication

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

Modular form 350658.2.a.ed

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.