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Properties

Label 201810cq
Number of curves $2$
Conductor $201810$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 201810cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
201810.g2 201810cq1 \([1, 1, 0, 93718142, -174627831788]\) \(111065142046871/80353879200\) \(-65860312360958216273239200\) \([]\) \(70308000\) \(3.6425\) \(\Gamma_0(N)\)-optimal
201810.g1 201810cq2 \([1, 1, 0, -1028359873, 15558476847733]\) \(-146737846222812889/42674688000000\) \(-34977381422880144665088000000\) \([]\) \(210924000\) \(4.1918\)  

Rank

sage: E.rank()
 

The elliptic curves in class 201810cq have rank \(1\).

Complex multiplication

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

Modular form 201810.2.a.cq

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.