Properties

Label 64400cg
Number of curves $2$
Conductor $64400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 64400cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.cf2 64400cg1 \([0, -1, 0, 6792, -435088]\) \(21653735/63112\) \(-100979200000000\) \([]\) \(207360\) \(1.3706\) \(\Gamma_0(N)\)-optimal
64400.cf1 64400cg2 \([0, -1, 0, -63208, 14124912]\) \(-17455277065/43606528\) \(-69770444800000000\) \([]\) \(622080\) \(1.9199\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64400cg have rank \(0\).

Complex multiplication

The elliptic curves in class 64400cg do not have complex multiplication.

Modular form 64400.2.a.cg

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