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Properties

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

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

Elliptic curves in class 116610q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116610.w2 116610q1 \([1, 1, 0, -560407, 163211989]\) \(-4032510095423809/57316147200\) \(-276654095150284800\) \([2]\) \(4128768\) \(2.1521\) \(\Gamma_0(N)\)-optimal
116610.w1 116610q2 \([1, 1, 0, -8996887, 10383163861]\) \(16685547865377876289/3300960000\) \(15933103436640000\) \([2]\) \(8257536\) \(2.4987\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116610.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} - q^{10} + 6 q^{11} - q^{12} - 4 q^{14} - q^{15} + q^{16} - 8 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.