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Properties

Label 121242k
Number of curves $2$
Conductor $121242$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 121242k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.r2 121242k1 \([1, 0, 1, -10409, 963884]\) \(-70393838689/186227712\) \(-329913751698432\) \([2]\) \(1036800\) \(1.4734\) \(\Gamma_0(N)\)-optimal
121242.r1 121242k2 \([1, 0, 1, -223369, 40574444]\) \(695718426450529/795171168\) \(1408694229553248\) \([2]\) \(2073600\) \(1.8199\)  

Rank

sage: E.rank()
 

The elliptic curves in class 121242k have rank \(1\).

Complex multiplication

The elliptic curves in class 121242k do not have complex multiplication.

Modular form 121242.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 4 q^{5} - q^{6} - q^{8} + q^{9} - 4 q^{10} + q^{12} - 6 q^{13} + 4 q^{15} + q^{16} - 4 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 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.