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Properties

Label 60690q
Number of curves $2$
Conductor $60690$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 60690q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.q2 60690q1 \([1, 0, 1, -389434, -94153768]\) \(-270601485933241/1951897500\) \(-47114060587177500\) \([2]\) \(884736\) \(2.0315\) \(\Gamma_0(N)\)-optimal
60690.q1 60690q2 \([1, 0, 1, -6241684, -6002585368]\) \(1114128841413009241/57352050\) \(1384339064166450\) \([2]\) \(1769472\) \(2.3780\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60690.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + 4 q^{13} + q^{14} - q^{15} + q^{16} - q^{18} + 6 q^{19} + O(q^{20})\) 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.