Properties

Label 5850.bd
Number of curves $2$
Conductor $5850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5850.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bd1 5850bz2 \([1, -1, 1, -2047055, 1039262447]\) \(666276475992821/58199166792\) \(82865610530015625000\) \([2]\) \(245760\) \(2.5625\)  
5850.bd2 5850bz1 \([1, -1, 1, -2002055, 1090832447]\) \(623295446073461/5458752\) \(7772324625000000\) \([2]\) \(122880\) \(2.2160\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 5850.bd do not have complex multiplication.

Modular form 5850.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{7} + q^{8} - 2 q^{11} - q^{13} - 4 q^{14} + q^{16} + 4 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.