Properties

Label 4641.d
Number of curves $2$
Conductor $4641$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4641.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4641.d1 4641g1 \([1, 0, 0, -455, 3696]\) \(10418796526321/6390657\) \(6390657\) \([2]\) \(2240\) \(0.24865\) \(\Gamma_0(N)\)-optimal
4641.d2 4641g2 \([1, 0, 0, -370, 5141]\) \(-5602762882081/8312741073\) \(-8312741073\) \([2]\) \(4480\) \(0.59522\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4641.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.