Properties

Label 60984.bw
Number of curves $4$
Conductor $60984$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.bw1 60984bx4 \([0, 0, 0, -273339, 54264870]\) \(1707831108/26411\) \(34927575581961216\) \([2]\) \(491520\) \(1.9756\)  
60984.bw2 60984bx2 \([0, 0, 0, -33759, -1078110]\) \(12869712/5929\) \(1960221078579456\) \([2, 2]\) \(245760\) \(1.6291\)  
60984.bw3 60984bx1 \([0, 0, 0, -28314, -1832787]\) \(121485312/77\) \(1591088537808\) \([2]\) \(122880\) \(1.2825\) \(\Gamma_0(N)\)-optimal
60984.bw4 60984bx3 \([0, 0, 0, 118701, -8121762]\) \(139863132/102487\) \(-135535286004636672\) \([2]\) \(491520\) \(1.9756\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60984.2.a.bw

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - q^{7} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.