Properties

Label 7623p
Number of curves 6
Conductor 7623
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("7623.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7623p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.g6 7623p1 [1, -1, 1, 1066, -3220] [2] 5120 \(\Gamma_0(N)\)-optimal
7623.g5 7623p2 [1, -1, 1, -4379, -22822] [2, 2] 10240  
7623.g2 7623p3 [1, -1, 1, -53384, -4727302] [2, 2] 20480  
7623.g3 7623p4 [1, -1, 1, -42494, 3361790] [2] 20480  
7623.g1 7623p5 [1, -1, 1, -853799, -303442180] [2] 40960  
7623.g4 7623p6 [1, -1, 1, -37049, -7687204] [2] 40960  

Rank

sage: E.rank()
 

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

Modular form 7623.2.a.g

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.