Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("4624.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4624.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4624.a1 4624f4 [0, 1, 0, -522608, 100312660] [2] 82944  
4624.a2 4624f3 [0, 1, 0, -476368, 126373524] [2] 41472  
4624.a3 4624f2 [0, 1, 0, -198928, -34208748] [2] 27648  
4624.a4 4624f1 [0, 1, 0, -13968, -398060] [2] 13824 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 4624.2.a.a

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

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.