Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("58800.cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.cu8 58800fc1 [0, -1, 0, 28992, 5824512] [2] 331776 \(\Gamma_0(N)\)-optimal
58800.cu6 58800fc2 [0, -1, 0, -363008, 76384512] [2, 2] 663552  
58800.cu7 58800fc3 [0, -1, 0, -265008, -171751488] [2] 995328  
58800.cu5 58800fc4 [0, -1, 0, -1343008, -515535488] [2] 1327104  
58800.cu4 58800fc5 [0, -1, 0, -5655008, 5177872512] [2] 1327104  
58800.cu3 58800fc6 [0, -1, 0, -6537008, -6418663488] [2, 2] 1990656  
58800.cu1 58800fc7 [0, -1, 0, -104537008, -411354663488] [2] 3981312  
58800.cu2 58800fc8 [0, -1, 0, -8889008, -1385383488] [2] 3981312  

Rank

sage: E.rank()
 

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

Modular form 58800.2.a.cu

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

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.