Properties

Label 60690bc
Number of curves $2$
Conductor $60690$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 60690bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.bc2 60690bc1 \([1, 0, 1, -2143678748, -38373422912422]\) \(-9186763300983704416553/47730830553907200\) \(-5660297838825981134399078400\) \([2]\) \(75202560\) \(4.1711\) \(\Gamma_0(N)\)-optimal
60690.bc1 60690bc2 \([1, 0, 1, -34341515548, -2449501992113062]\) \(37769548376817211811066153/1011738331054080\) \(119979900250322138867957760\) \([2]\) \(150405120\) \(4.5176\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60690bc have rank \(1\).

Complex multiplication

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

Modular form 60690.2.a.bc

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 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.