Properties

Label 236992.v
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.v1 236992v2 \([0, 1, 0, -796321, 118232127]\) \(5756278756/2705927\) \(26252037915548254208\) \([2]\) \(8110080\) \(2.4205\)  
236992.v2 236992v1 \([0, 1, 0, 177039, 14082607]\) \(253012016/181447\) \(-440085183715459072\) \([2]\) \(4055040\) \(2.0739\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.v have rank \(0\).

Complex multiplication

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

Modular form 236992.2.a.v

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + 4q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} - 8q^{15} + 4q^{17} + O(q^{20})\)  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 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.