Properties

Label 60984.bf
Number of curves $2$
Conductor $60984$
CM no
Rank $1$
Graph

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

Elliptic curves in class 60984.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.bf1 60984a1 \([0, 0, 0, -59895, -5475734]\) \(1458000/49\) \(798608587569408\) \([2]\) \(202752\) \(1.6320\) \(\Gamma_0(N)\)-optimal
60984.bf2 60984a2 \([0, 0, 0, 19965, -19004018]\) \(13500/2401\) \(-156527283163603968\) \([2]\) \(405504\) \(1.9786\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60984.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 60984.bf do not have complex multiplication.

Modular form 60984.2.a.bf

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