Properties

Label 60984.n
Number of curves $4$
Conductor $60984$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.n1 60984cj4 \([0, 0, 0, -41417211, -102593328266]\) \(2970658109581346/2139291\) \(5658267244277716992\) \([2]\) \(3932160\) \(2.9102\)  
60984.n2 60984cj3 \([0, 0, 0, -5959371, 3325756390]\) \(8849350367426/3314597517\) \(8766866479784822728704\) \([2]\) \(3932160\) \(2.9102\)  
60984.n3 60984cj2 \([0, 0, 0, -2605251, -1581321170]\) \(1478729816932/38900169\) \(51444041986239243264\) \([2, 2]\) \(1966080\) \(2.5636\)  
60984.n4 60984cj1 \([0, 0, 0, 30129, -79681646]\) \(9148592/8301447\) \(-2744589541593892608\) \([2]\) \(983040\) \(2.2170\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60984.2.a.n

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - 6q^{13} + 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.