Properties

Label 274014q
Number of curves 3
Conductor 274014
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("274014.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 274014q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
274014.q2 274014q1 [1, -1, 1, -320405, -78749395] [] 2674944 \(\Gamma_0(N)\)-optimal
274014.q3 274014q2 [1, -1, 1, 2151220, 292231631] [3] 8024832  
274014.q1 274014q3 [1, -1, 1, -34155635, 79795201619] [3] 24074496  

Rank

sage: E.rank()
 

The elliptic curves in class 274014q have rank \(1\).

Modular form 274014.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{11} + q^{13} - q^{14} + q^{16} + 3q^{17} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.