Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.i1 236992i2 \([0, 1, 0, -5891649, 5495580607]\) \(582810602977/829472\) \(32189087723187863552\) \([2]\) \(8110080\) \(2.6461\)  
236992.i2 236992i1 \([0, 1, 0, -474689, 32034751]\) \(304821217/164864\) \(6397831100260941824\) \([2]\) \(4055040\) \(2.2995\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.i

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