Properties

Label 405600gq
Number of curves $2$
Conductor $405600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405600gq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.gq2 405600gq1 \([0, 1, 0, -33518, 2348568]\) \(107850176/117\) \(4517893224000\) \([2]\) \(1204224\) \(1.3438\) \(\Gamma_0(N)\)-optimal
405600.gq1 405600gq2 \([0, 1, 0, -41968, 1064168]\) \(26463592/13689\) \(4228748057664000\) \([2]\) \(2408448\) \(1.6904\)  

Rank

sage: E.rank()
 

The elliptic curves in class 405600gq have rank \(0\).

Complex multiplication

The elliptic curves in class 405600gq do not have complex multiplication.

Modular form 405600.2.a.gq

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4q^{7} + q^{9} - 2q^{11} + 2q^{19} + O(q^{20})\)  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.