Properties

Label 64400bu
Number of curves $2$
Conductor $64400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.l2 64400bu1 \([0, 1, 0, 272, -3372]\) \(21653735/63112\) \(-6462668800\) \([]\) \(41472\) \(0.56587\) \(\Gamma_0(N)\)-optimal
64400.l1 64400bu2 \([0, 1, 0, -2528, 111988]\) \(-17455277065/43606528\) \(-4465308467200\) \([]\) \(124416\) \(1.1152\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64400bu have rank \(1\).

Complex multiplication

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

Modular form 64400.2.a.bu

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