Properties

Label 4410.p
Number of curves 4
Conductor 4410
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4410.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.p1 4410d3 [1, -1, 0, -20589, 1001573] [2] 13824  
4410.p2 4410d1 [1, -1, 0, -5154, -140960] [2] 4608 \(\Gamma_0(N)\)-optimal
4410.p3 4410d2 [1, -1, 0, -3684, -224162] [2] 9216  
4410.p4 4410d4 [1, -1, 0, 32331, 5266925] [2] 27648  

Rank

sage: E.rank()
 

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

Modular form 4410.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2q^{13} + q^{16} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.