Properties

Label 58800.k
Number of curves $2$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.k1 58800bh2 \([0, -1, 0, -122908, -15676688]\) \(1272112/75\) \(12106082100000000\) \([2]\) \(516096\) \(1.8393\)  
58800.k2 58800bh1 \([0, -1, 0, 5717, -1013438]\) \(2048/45\) \(-453978078750000\) \([2]\) \(258048\) \(1.4927\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 58800.2.a.k

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