Properties

Label 62400gk
Number of curves $2$
Conductor $62400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400gk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.gt2 62400gk1 \([0, 1, 0, 6367, 544863]\) \(6967871/35100\) \(-143769600000000\) \([2]\) \(221184\) \(1.3988\) \(\Gamma_0(N)\)-optimal
62400.gt1 62400gk2 \([0, 1, 0, -73633, 6864863]\) \(10779215329/1232010\) \(5046312960000000\) \([2]\) \(442368\) \(1.7454\)  

Rank

sage: E.rank()
 

The elliptic curves in class 62400gk have rank \(1\).

Complex multiplication

The elliptic curves in class 62400gk do not have complex multiplication.

Modular form 62400.2.a.gk

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{7} + q^{9} + 4q^{11} - q^{13} - 8q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.