Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 60690.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.f1 60690l2 \([1, 1, 0, -118828773, -498624543603]\) \(37769548376817211811066153/1011738331054080\) \(4970670420468695040\) \([2]\) \(8847360\) \(3.1010\)  
60690.f2 60690l1 \([1, 1, 0, -7417573, -7813643123]\) \(-9186763300983704416553/47730830553907200\) \(-234501570511346073600\) \([2]\) \(4423680\) \(2.7545\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60690.2.a.f

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