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Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 121242s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.w2 121242s1 \([1, 1, 1, -6113, 225083]\) \(-14260515625/4382748\) \(-7764305429628\) \([2]\) \(276480\) \(1.1870\) \(\Gamma_0(N)\)-optimal
121242.w1 121242s2 \([1, 1, 1, -104123, 12887975]\) \(70470585447625/4518018\) \(8003944486098\) \([2]\) \(552960\) \(1.5336\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 121242.2.a.s

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