Properties

Label 350064co
Number of curves $2$
Conductor $350064$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 350064co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.co1 350064co1 \([0, 0, 0, -5681883, 4464288650]\) \(6793805286030262681/1048227429629952\) \(3129990333236162592768\) \([2]\) \(28901376\) \(2.8480\) \(\Gamma_0(N)\)-optimal
350064.co2 350064co2 \([0, 0, 0, 9893157, 24633965450]\) \(35862531227445945959/108547797844556928\) \(-324121987599081474097152\) \([2]\) \(57802752\) \(3.1946\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350064co have rank \(1\).

Complex multiplication

The elliptic curves in class 350064co do not have complex multiplication.

Modular form 350064.2.a.co

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + 2 q^{7} + q^{11} - q^{13} + q^{17} + 4 q^{19} + O(q^{20})\)  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.