Properties

Label 58800gh
Number of curves $2$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.a2 58800gh1 \([0, -1, 0, -28408, -1820048]\) \(505318200625/4251528\) \(21332466892800\) \([]\) \(207360\) \(1.3831\) \(\Gamma_0(N)\)-optimal
58800.a1 58800gh2 \([0, -1, 0, -2296408, -1338669968]\) \(266916252066900625/162\) \(812851200\) \([]\) \(622080\) \(1.9324\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 58800.2.a.gh

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6q^{11} - 4q^{13} - 3q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.