Properties

Label 218010p
Number of curves $2$
Conductor $218010$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 218010p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
218010.cb2 218010p1 \([1, 0, 0, -6341, 129921]\) \(5841725401/1857600\) \(8966280398400\) \([2]\) \(663552\) \(1.1892\) \(\Gamma_0(N)\)-optimal
218010.cb1 218010p2 \([1, 0, 0, -40141, -2999959]\) \(1481933914201/53916840\) \(260246288563560\) \([2]\) \(1327104\) \(1.5358\)  

Rank

sage: E.rank()
 

The elliptic curves in class 218010p have rank \(1\).

Complex multiplication

The elliptic curves in class 218010p do not have complex multiplication.

Modular form 218010.2.a.p

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