Properties

Label 4641.c
Number of curves $4$
Conductor $4641$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4641.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4641.c1 4641a3 \([1, 1, 1, -24752, -1509184]\) \(1677087406638588673/4641\) \(4641\) \([2]\) \(5120\) \(0.82194\)  
4641.c2 4641a2 \([1, 1, 1, -1547, -24064]\) \(409460675852593/21538881\) \(21538881\) \([2, 2]\) \(2560\) \(0.47537\)  
4641.c3 4641a4 \([1, 1, 1, -1462, -26716]\) \(-345608484635233/94427721297\) \(-94427721297\) \([2]\) \(5120\) \(0.82194\)  
4641.c4 4641a1 \([1, 1, 1, -102, -366]\) \(117433042273/22801233\) \(22801233\) \([4]\) \(1280\) \(0.12880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4641.c have rank \(1\).

Complex multiplication

The elliptic curves in class 4641.c do not have complex multiplication.

Modular form 4641.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + 2q^{5} + q^{6} - q^{7} + 3q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} + q^{13} + q^{14} - 2q^{15} - q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.