Properties

Label 296450.gq
Number of curves 4
Conductor 296450
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("296450.gq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 296450.gq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
296450.gq1 296450gq4 [1, 0, 0, -3871047188, -90075862264508] [2] 477757440  
296450.gq2 296450gq2 [1, 0, 0, -530055688, 4655337028992] [2] 159252480  
296450.gq3 296450gq1 [1, 0, 0, -8303688, 179226620992] [2] 79626240 \(\Gamma_0(N)\)-optimal
296450.gq4 296450gq3 [1, 0, 0, 74702312, -4827944317008] [2] 238878720  

Rank

sage: E.rank()
 

The elliptic curves in class 296450.gq have rank \(0\).

Modular form 296450.2.a.gq

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.