Properties

Label 7623.f
Number of curves 6
Conductor 7623
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7623.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7623.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.f1 7623i5 [1, -1, 1, -4921214, -4200771594] [2] 153600  
7623.f2 7623i3 [1, -1, 1, -309299, -64806222] [2, 2] 76800  
7623.f3 7623i2 [1, -1, 1, -42494, 1895028] [2, 2] 38400  
7623.f4 7623i1 [1, -1, 1, -37049, 2753160] [4] 19200 \(\Gamma_0(N)\)-optimal
7623.f5 7623i6 [1, -1, 1, 33736, -200922510] [2] 153600  
7623.f6 7623i4 [1, -1, 1, 137191, 13610490] [2] 76800  

Rank

sage: E.rank()
 

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

Modular form 7623.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + 2q^{5} - q^{7} + 3q^{8} - 2q^{10} - 6q^{13} + q^{14} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.