Properties

Label 58800hf
Number of curves $4$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800hf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.x4 58800hf1 \([0, -1, 0, -59208, -7523088]\) \(-24389/12\) \(-11294304000000000\) \([2]\) \(345600\) \(1.7855\) \(\Gamma_0(N)\)-optimal
58800.x2 58800hf2 \([0, -1, 0, -1039208, -407363088]\) \(131872229/18\) \(16941456000000000\) \([2]\) \(691200\) \(2.1321\)  
58800.x3 58800hf3 \([0, -1, 0, -549208, 752956912]\) \(-19465109/248832\) \(-234198687744000000000\) \([2]\) \(1728000\) \(2.5903\)  
58800.x1 58800hf4 \([0, -1, 0, -16229208, 25088316912]\) \(502270291349/1889568\) \(1778446285056000000000\) \([2]\) \(3456000\) \(2.9368\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800hf have rank \(0\).

Complex multiplication

The elliptic curves in class 58800hf do not have complex multiplication.

Modular form 58800.2.a.hf

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 2q^{11} - 6q^{13} - 2q^{17} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.