Properties

Label 1584.h
Number of curves $4$
Conductor $1584$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 1584.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1584.h1 1584l3 \([0, 0, 0, -11595, -478726]\) \(57736239625/255552\) \(763074183168\) \([2]\) \(2304\) \(1.1324\)  
1584.h2 1584l4 \([0, 0, 0, -5835, -954502]\) \(-7357983625/127552392\) \(-380869401673728\) \([2]\) \(4608\) \(1.4790\)  
1584.h3 1584l1 \([0, 0, 0, -795, 8138]\) \(18609625/1188\) \(3547348992\) \([2]\) \(768\) \(0.58307\) \(\Gamma_0(N)\)-optimal
1584.h4 1584l2 \([0, 0, 0, 645, 34346]\) \(9938375/176418\) \(-526781325312\) \([2]\) \(1536\) \(0.92964\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1584.2.a.h

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