Properties

Label 7623.k
Number of curves 2
Conductor 7623
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7623.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7623.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.k1 7623e2 [0, 0, 1, -3036, -64386] [] 4608  
7623.k2 7623e1 [0, 0, 1, -66, 63] [] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7623.k have rank \(1\).

Modular form 7623.2.a.k

sage: E.q_eigenform(10)
 
\( q - 2q^{4} + 3q^{5} - q^{7} + 4q^{13} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.