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Properties

Label 60690n
Number of curves $2$
Conductor $60690$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 60690n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.o2 60690n1 \([1, 1, 0, 54815058, 221034882996]\) \(153597108917748007/266827932000000\) \(-31642557845965914204000000\) \([2]\) \(17547264\) \(3.5779\) \(\Gamma_0(N)\)-optimal
60690.o1 60690n2 \([1, 1, 0, -387354942, 2293131936996]\) \(54201427552325291993/12208015311282000\) \(1447722612007794826739154000\) \([2]\) \(35094528\) \(3.9245\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60690n have rank \(0\).

Complex multiplication

The elliptic curves in class 60690n do not have complex multiplication.

Modular form 60690.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} - 4 q^{13} + q^{14} - q^{15} + q^{16} - q^{18} + O(q^{20})\) Copy content 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 Cremona 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 Cremona labels.