Properties

Label 4624.a
Number of curves $4$
Conductor $4624$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 4624.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4624.a1 4624f4 \([0, 1, 0, -522608, 100312660]\) \(159661140625/48275138\) \(4772841367386202112\) \([2]\) \(82944\) \(2.2892\)  
4624.a2 4624f3 \([0, 1, 0, -476368, 126373524]\) \(120920208625/19652\) \(1942943768526848\) \([2]\) \(41472\) \(1.9427\)  
4624.a3 4624f2 \([0, 1, 0, -198928, -34208748]\) \(8805624625/2312\) \(228581619826688\) \([2]\) \(27648\) \(1.7399\)  
4624.a4 4624f1 \([0, 1, 0, -13968, -398060]\) \(3048625/1088\) \(107567821094912\) \([2]\) \(13824\) \(1.3934\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4624.a have rank \(0\).

Complex multiplication

The elliptic curves in class 4624.a do not have complex multiplication.

Modular form 4624.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 4 q^{7} + q^{9} + 6 q^{11} + 2 q^{13} + 4 q^{19} + O(q^{20})\) 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.