Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.ch2 236992ch1 \([0, -1, 0, -59953, 7280529]\) \(-9826000/3703\) \(-8981330279907328\) \([2]\) \(1351680\) \(1.7710\) \(\Gamma_0(N)\)-optimal
236992.ch1 236992ch2 \([0, -1, 0, -1033313, 404606081]\) \(12576878500/1127\) \(10933793384235008\) \([2]\) \(2703360\) \(2.1176\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.ch

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