Properties

Label 4410n
Number of curves 2
Conductor 4410
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4410.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.r1 4410n1 [1, -1, 0, -58074, -5372200] [] 11760 \(\Gamma_0(N)\)-optimal
4410.r2 4410n2 [1, -1, 0, 404976, 51008768] [] 82320  

Rank

sage: E.rank()
 

The elliptic curves in class 4410n have rank \(1\).

Modular form 4410.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 2q^{11} + q^{16} + 4q^{17} - 6q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.