Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 1584.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1584.p1 1584o2 \([0, 0, 0, -696, -7108]\) \(-199794688/1331\) \(-248396544\) \([]\) \(720\) \(0.44632\)  
1584.p2 1584o1 \([0, 0, 0, 24, -52]\) \(8192/11\) \(-2052864\) \([]\) \(240\) \(-0.10299\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1584.2.a.p

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} - 2 q^{7} - q^{11} - 4 q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.