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Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 116610.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116610.g1 116610g2 \([1, 1, 0, -153192588, -729695881182]\) \(82371478639106274806161/22131985839843750\) \(106826868439630371093750\) \([2]\) \(25804800\) \(3.4023\)  
116610.g2 116610g1 \([1, 1, 0, -8388318, -14333826528]\) \(-13523476093748990641/10553516202937500\) \(-50939806989984551437500\) \([2]\) \(12902400\) \(3.0557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116610.2.a.g

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