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Properties

Label 102850.bf
Number of curves $2$
Conductor $102850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 102850.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102850.bf1 102850be2 \([1, -1, 0, -2327, -42619]\) \(8377795791/2312\) \(384659000\) \([2]\) \(55296\) \(0.62951\)  
102850.bf2 102850be1 \([1, -1, 0, -127, -819]\) \(-1367631/1088\) \(-181016000\) \([2]\) \(27648\) \(0.28294\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102850.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 102850.bf do not have complex multiplication.

Modular form 102850.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{7} - q^{8} - 3 q^{9} - 2 q^{13} - 2 q^{14} + q^{16} - q^{17} + 3 q^{18} + 2 q^{19} + O(q^{20})\) 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.