Properties

Label 1584.r
Number of curves $2$
Conductor $1584$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1584.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1584.r1 1584i2 \([0, 0, 0, -2403, 45090]\) \(19034163/121\) \(9755209728\) \([2]\) \(1536\) \(0.75376\)  
1584.r2 1584i1 \([0, 0, 0, -243, -270]\) \(19683/11\) \(886837248\) \([2]\) \(768\) \(0.40719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1584.r have rank \(0\).

Complex multiplication

The elliptic curves in class 1584.r do not have complex multiplication.

Modular form 1584.2.a.r

sage: E.q_eigenform(10)
 
\(q + 4q^{5} + 2q^{7} - q^{11} - 2q^{13} - 2q^{17} + 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.