Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("kg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800kg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.fh2 58800kg1 \([0, 1, 0, 19192, -76812]\) \(2595575/1512\) \(-455386337280000\) \([]\) \(248832\) \(1.5021\) \(\Gamma_0(N)\)-optimal
58800.fh1 58800kg2 \([0, 1, 0, -274808, -58759212]\) \(-7620530425/526848\) \(-158676839301120000\) \([]\) \(746496\) \(2.0514\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 58800.2.a.kg

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