Properties

Label 7623.n
Number of curves 2
Conductor 7623
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7623.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7623.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.n1 7623o2 [1, -1, 0, -56106, 4735957] [2] 34560  
7623.n2 7623o1 [1, -1, 0, 3789, 339664] [2] 17280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7623.n have rank \(0\).

Modular form 7623.2.a.n

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + 2q^{5} + q^{7} - 3q^{8} + 2q^{10} - 4q^{13} + q^{14} - q^{16} + 4q^{17} + O(q^{20}) \)

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.