Properties

Label 201810ce
Number of curves $2$
Conductor $201810$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 201810ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
201810.n2 201810ce1 \([1, 1, 0, -289947, 59936481]\) \(2805165723497909881/1953492187500\) \(1877305992187500\) \([]\) \(2643840\) \(1.8674\) \(\Gamma_0(N)\)-optimal
201810.n1 201810ce2 \([1, 1, 0, -23481822, 43787362356]\) \(1490032455664120989539881/504000\) \(484344000\) \([]\) \(7931520\) \(2.4167\)  

Rank

sage: E.rank()
 

The elliptic curves in class 201810ce have rank \(2\).

Complex multiplication

The elliptic curves in class 201810ce do not have complex multiplication.

Modular form 201810.2.a.ce

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.