Properties

Label 60333.n
Number of curves $2$
Conductor $60333$
CM no
Rank $1$
Graph

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

Elliptic curves in class 60333.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60333.n1 60333l1 \([1, 0, 1, -76899, 8197009]\) \(10418796526321/6390657\) \(30846480723513\) \([2]\) \(376320\) \(1.5311\) \(\Gamma_0(N)\)-optimal
60333.n2 60333l2 \([1, 0, 1, -62534, 11357309]\) \(-5602762882081/8312741073\) \(-40124013425826057\) \([2]\) \(752640\) \(1.8777\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60333.n have rank \(1\).

Complex multiplication

The elliptic curves in class 60333.n do not have complex multiplication.

Modular form 60333.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + 4q^{5} + q^{6} - q^{7} - 3q^{8} + q^{9} + 4q^{10} + 4q^{11} - q^{12} - q^{14} + 4q^{15} - q^{16} + q^{17} + q^{18} + O(q^{20})\)  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.