Properties

Label 1584.i
Number of curves $4$
Conductor $1584$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 1584.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1584.i1 1584h4 \([0, 0, 0, -147555, 21816162]\) \(4406910829875/7744\) \(624333422592\) \([2]\) \(4608\) \(1.5225\)  
1584.i2 1584h3 \([0, 0, 0, -9315, 333666]\) \(1108717875/45056\) \(3632485367808\) \([2]\) \(2304\) \(1.1759\)  
1584.i3 1584h2 \([0, 0, 0, -2355, 10994]\) \(13060888875/7086244\) \(783681896448\) \([2]\) \(1536\) \(0.97321\)  
1584.i4 1584h1 \([0, 0, 0, -1395, -19918]\) \(2714704875/21296\) \(2355167232\) \([2]\) \(768\) \(0.62663\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1584.2.a.i

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.