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Properties

Label 4410.bg
Number of curves $2$
Conductor $4410$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 4410.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.bg1 4410bl2 \([1, -1, 1, -1427, -35661]\) \(-8990558521/10485760\) \(-374561832960\) \([]\) \(6048\) \(0.91483\)  
4410.bg2 4410bl1 \([1, -1, 1, 148, 879]\) \(10100279/16000\) \(-571536000\) \([]\) \(2016\) \(0.36553\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4410.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 3 q^{11} + q^{13} + q^{16} - 6 q^{17} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.