Properties

Label 249090.bd
Number of curves $2$
Conductor $249090$
CM no
Rank $0$
Graph

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

Elliptic curves in class 249090.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.bd1 249090bd2 \([1, 0, 1, -41884, -3169054]\) \(172715635009/7935000\) \(373309065735000\) \([2]\) \(1382400\) \(1.5578\)  
249090.bd2 249090bd1 \([1, 0, 1, 1436, -188638]\) \(6967871/331200\) \(-15581595787200\) \([2]\) \(691200\) \(1.2112\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 249090.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 249090.bd do not have complex multiplication.

Modular form 249090.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + 6 q^{13} + 2 q^{14} - q^{15} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.