Properties

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

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Show commands: SageMath
E = EllipticCurve("ke1")
 
E.isogeny_class()
 

Elliptic curves in class 58800.ke

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.ke1 58800kf1 \([0, 1, 0, -14128, 620948]\) \(5177717/189\) \(11384658432000\) \([2]\) \(147456\) \(1.2749\) \(\Gamma_0(N)\)-optimal
58800.ke2 58800kf2 \([0, 1, 0, 5472, 2228148]\) \(300763/35721\) \(-2151700443648000\) \([2]\) \(294912\) \(1.6215\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 58800.2.a.ke

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 6 q^{11} + 2 q^{13} - 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.