Properties

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

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

Elliptic curves in class 236992.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.g1 236992g2 \([0, 1, 0, -11934945, 15866079679]\) \(38758598383688/25921\) \(125738623918702592\) \([2]\) \(15138816\) \(2.5974\)  
236992.g2 236992g1 \([0, 1, 0, -741305, 250951879]\) \(-74299881664/1958887\) \(-1187780929517744128\) \([2]\) \(7569408\) \(2.2508\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - 4q^{5} + q^{7} + q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 6q^{17} + 2q^{19} + O(q^{20})\)  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 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.