Properties

Label 6630q
Number of curves 2
Conductor 6630
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6630.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6630q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6630.s1 6630q1 [1, 1, 1, -13620, 599157] [2] 15360 \(\Gamma_0(N)\)-optimal
6630.s2 6630q2 [1, 1, 1, -2100, 1594485] [2] 30720  

Rank

sage: E.rank()
 

The elliptic curves in class 6630q have rank \(1\).

Modular form 6630.2.a.s

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

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.