Properties

Label 279312.cx
Number of curves 2
Conductor 279312
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("279312.cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 279312.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
279312.cx1 279312cx2 [0, 1, 0, -10478608, -12957731116] [2] 10813440  
279312.cx2 279312cx1 [0, 1, 0, -194848, -481473484] [2] 5406720 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 279312.cx have rank \(1\).

Modular form 279312.2.a.cx

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{7} + q^{9} + q^{11} + 2q^{13} + 2q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.