Properties

Label 20286bf
Number of curves $2$
Conductor $20286$
CM no
Rank $2$
Graph

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

Elliptic curves in class 20286bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.d2 20286bf1 \([1, -1, 0, 1314, 80716]\) \(2924207/34776\) \(-2982602623896\) \([]\) \(46080\) \(1.0746\) \(\Gamma_0(N)\)-optimal
20286.d1 20286bf2 \([1, -1, 0, -11916, -2282162]\) \(-2181825073/25039686\) \(-2147556739278006\) \([]\) \(138240\) \(1.6239\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20286bf have rank \(2\).

Complex multiplication

The elliptic curves in class 20286bf do not have complex multiplication.

Modular form 20286.2.a.bf

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.