Properties

Label 240669bd
Number of curves $2$
Conductor $240669$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 240669bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
240669.bd2 240669bd1 \([1, -1, 0, -285885, -58710272]\) \(2000852317801/2094417\) \(2704872469229073\) \([2]\) \(2488320\) \(1.8784\) \(\Gamma_0(N)\)-optimal
240669.bd1 240669bd2 \([1, -1, 0, -356670, -27352517]\) \(3885442650361/1996623837\) \(2578575731627377053\) \([2]\) \(4976640\) \(2.2250\)  

Rank

sage: E.rank()
 

The elliptic curves in class 240669bd have rank \(1\).

Complex multiplication

The elliptic curves in class 240669bd do not have complex multiplication.

Modular form 240669.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 4 q^{5} - 2 q^{7} - 3 q^{8} + 4 q^{10} + q^{13} - 2 q^{14} - q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.