Properties

Label 4410be
Number of curves $4$
Conductor $4410$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.bc3 4410be1 [1, -1, 1, -1553, -14479] [2] 6144 \(\Gamma_0(N)\)-optimal
4410.bc2 4410be2 [1, -1, 1, -10373, 398297] [2, 2] 12288  
4410.bc1 4410be3 [1, -1, 1, -164723, 25773437] [2] 24576  
4410.bc4 4410be4 [1, -1, 1, 2857, 1334981] [2] 24576  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4410.2.a.be

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4q^{11} + 2q^{13} + q^{16} - 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.