Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 64400e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.d1 64400e1 \([0, 1, 0, -1008, -2012]\) \(7086244/4025\) \(64400000000\) \([2]\) \(49152\) \(0.76392\) \(\Gamma_0(N)\)-optimal
64400.d2 64400e2 \([0, 1, 0, 3992, -12012]\) \(219804478/129605\) \(-4147360000000\) \([2]\) \(98304\) \(1.1105\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64400.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.