Properties

Label 1584m
Number of curves $2$
Conductor $1584$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 1584m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1584.c2 1584m1 \([0, 0, 0, -696, 8215]\) \(-3196715008/649539\) \(-7576222896\) \([2]\) \(960\) \(0.61810\) \(\Gamma_0(N)\)-optimal
1584.c1 1584m2 \([0, 0, 0, -11631, 482794]\) \(932410994128/29403\) \(5487305472\) \([2]\) \(1920\) \(0.96467\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1584m have rank \(1\).

Complex multiplication

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

Modular form 1584.2.a.m

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