Properties

Label 63210ct
Number of curves $2$
Conductor $63210$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63210ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63210.cm2 63210ct1 [1, 0, 0, -502545, 142151337] [2] 1451520 \(\Gamma_0(N)\)-optimal
63210.cm1 63210ct2 [1, 0, 0, -8123025, 8910275625] [2] 2903040  

Rank

sage: E.rank()
 

The elliptic curves in class 63210ct have rank \(1\).

Complex multiplication

The elliptic curves in class 63210ct do not have complex multiplication.

Modular form 63210.2.a.ct

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

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.