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Properties

Label 116242.g
Number of curves $3$
Conductor $116242$
CM no
Rank $1$
Graph

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

Elliptic curves in class 116242.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.g1 116242j3 \([1, 1, 0, -11449844, 18070943404]\) \(-3528587363533685713/958213215898316\) \(-45079984927779482636396\) \([]\) \(10264320\) \(3.0630\)  
116242.g2 116242j1 \([1, 1, 0, -237184, -45531136]\) \(-31366144171153/801898496\) \(-37726021216894976\) \([]\) \(1140480\) \(1.9644\) \(\Gamma_0(N)\)-optimal
116242.g3 116242j2 \([1, 1, 0, 1033536, -189168704]\) \(2595244476505967/1831970200256\) \(-86186652036789945536\) \([]\) \(3421440\) \(2.5137\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116242.g have rank \(1\).

Complex multiplication

The elliptic curves in class 116242.g do not have complex multiplication.

Modular form 116242.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} - q^{8} - 2 q^{9} + 3 q^{10} - q^{12} - 5 q^{13} - q^{14} + 3 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.