Properties

Label 28050bf
Number of curves $2$
Conductor $28050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 28050bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.bs2 28050bf1 \([1, 0, 1, -5001, -116852]\) \(885012508801/137332800\) \(2145825000000\) \([2]\) \(55296\) \(1.0895\) \(\Gamma_0(N)\)-optimal
28050.bs1 28050bf2 \([1, 0, 1, -22001, 1141148]\) \(75370704203521/7497765000\) \(117152578125000\) \([2]\) \(110592\) \(1.4361\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28050bf have rank \(1\).

Complex multiplication

The elliptic curves in class 28050bf do not have complex multiplication.

Modular form 28050.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 4 q^{13} - 2 q^{14} + q^{16} - q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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 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.