Properties

Label 236992s
Number of curves $2$
Conductor $236992$
CM no
Rank $1$
Graph

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

Elliptic curves in class 236992s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.s2 236992s1 \([0, 1, 0, -337, 1455]\) \(21296/7\) \(1395408896\) \([2]\) \(86016\) \(0.45770\) \(\Gamma_0(N)\)-optimal
236992.s1 236992s2 \([0, 1, 0, -2177, -38657]\) \(1431644/49\) \(39071449088\) \([2]\) \(172032\) \(0.80427\)  

Rank

sage: E.rank()
 

The elliptic curves in class 236992s have rank \(1\).

Complex multiplication

The elliptic curves in class 236992s do not have complex multiplication.

Modular form 236992.2.a.s

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{5} - q^{7} + q^{9} + 2 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.