Properties

Label 4410.n
Number of curves $2$
Conductor $4410$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.n1 4410q1 \([1, -1, 0, -6624, -77652]\) \(1092727/540\) \(15885600931620\) \([2]\) \(10752\) \(1.2261\) \(\Gamma_0(N)\)-optimal
4410.n2 4410q2 \([1, -1, 0, 24246, -614790]\) \(53582633/36450\) \(-1072278062884350\) \([2]\) \(21504\) \(1.5727\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4410.n have rank \(0\).

Complex multiplication

The elliptic curves in class 4410.n do not have complex multiplication.

Modular form 4410.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2q^{11} - 2q^{13} + q^{16} - 4q^{17} + O(q^{20})\)  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.