Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bc1 64400b1 \([0, 0, 0, -1175, -14250]\) \(44851536/4025\) \(16100000000\) \([2]\) \(30720\) \(0.69821\) \(\Gamma_0(N)\)-optimal
64400.bc2 64400b2 \([0, 0, 0, 1325, -66750]\) \(16078716/129605\) \(-2073680000000\) \([2]\) \(61440\) \(1.0448\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64400.2.a.b

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