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Properties

Label 116610bc
Number of curves $2$
Conductor $116610$
CM no
Rank $0$
Graph

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

Elliptic curves in class 116610bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116610.x2 116610bc1 \([1, 0, 1, 184206, 199498756]\) \(24202766345041271/615905596592640\) \(-17590879744282391040\) \([3]\) \(3919104\) \(2.3730\) \(\Gamma_0(N)\)-optimal
116610.x1 116610bc2 \([1, 0, 1, -1663809, -5495344268]\) \(-17834475240600567289/446428782526464000\) \(-12750452457738338304000\) \([]\) \(11757312\) \(2.9223\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116610bc have rank \(0\).

Complex multiplication

The elliptic curves in class 116610bc do not have complex multiplication.

Modular form 116610.2.a.bc

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.