Properties

Label 60984.bi
Number of curves $2$
Conductor $60984$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.bi1 60984bd2 \([0, 0, 0, -386595, 25227774]\) \(2415899250/1294139\) \(3422902407032199168\) \([2]\) \(737280\) \(2.2476\)  
60984.bi2 60984bd1 \([0, 0, 0, 92565, 3090582]\) \(66325500/41503\) \(-54886190200224768\) \([2]\) \(368640\) \(1.9011\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 60984.bi have rank \(0\).

Complex multiplication

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

Modular form 60984.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{7} + 6q^{13} + 2q^{19} + O(q^{20})\)  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.