Properties

Label 58800fz
Number of curves 8
Conductor 58800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.ei1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800fz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.ei7 58800fz1 [0, -1, 0, 4115592, 2420211312] [2] 3538944 \(\Gamma_0(N)\)-optimal
58800.ei6 58800fz2 [0, -1, 0, -20972408, 21687795312] [2, 2] 7077888  
58800.ei5 58800fz3 [0, -1, 0, -147980408, -677364236688] [2, 2] 14155776  
58800.ei4 58800fz4 [0, -1, 0, -295372408, 1953463795312] [2] 14155776  
58800.ei8 58800fz5 [0, -1, 0, 24891592, -2165446412688] [2] 28311552  
58800.ei2 58800fz6 [0, -1, 0, -2352980408, -43930644236688] [2, 2] 28311552  
58800.ei3 58800fz7 [0, -1, 0, -2338280408, -44506649036688] [2] 56623104  
58800.ei1 58800fz8 [0, -1, 0, -37647680408, -2811599839436688] [2] 56623104  

Rank

sage: E.rank()
 

The elliptic curves in class 58800fz have rank \(1\).

Modular form 58800.2.a.ei

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} + 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.