Properties

Label 7623f
Number of curves 3
Conductor 7623
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7623.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7623f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.i1 7623f1 [0, 0, 1, -97284, 11679192] [] 24000 \(\Gamma_0(N)\)-optimal
7623.i2 7623f2 [0, 0, 1, -53724, 22160817] [] 72000  
7623.i3 7623f3 [0, 0, 1, 479886, -573614748] [] 216000  

Rank

sage: E.rank()
 

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

Modular form 7623.2.a.i

sage: E.q_eigenform(10)
 
\( q - 2q^{4} - 3q^{5} - q^{7} + 4q^{13} + 4q^{16} - 6q^{17} - 2q^{19} + O(q^{20}) \)

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.