Properties

Label 4800bp
Number of curves 8
Conductor 4800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4800.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.d8 4800bp1 [0, -1, 0, 2367, -136863] [2] 9216 \(\Gamma_0(N)\)-optimal
4800.d6 4800bp2 [0, -1, 0, -29633, -1768863] [2, 2] 18432  
4800.d7 4800bp3 [0, -1, 0, -21633, 4015137] [2] 27648  
4800.d4 4800bp4 [0, -1, 0, -461633, -120568863] [2] 36864  
4800.d5 4800bp5 [0, -1, 0, -109633, 12071137] [2] 36864  
4800.d3 4800bp6 [0, -1, 0, -533633, 149935137] [2, 2] 55296  
4800.d2 4800bp7 [0, -1, 0, -725633, 32623137] [2] 110592  
4800.d1 4800bp8 [0, -1, 0, -8533633, 9597935137] [2] 110592  

Rank

sage: E.rank()
 

The elliptic curves in class 4800bp have rank \(0\).

Modular form 4800.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.