Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.r2 236992r1 \([0, 1, 0, -59953, -7280529]\) \(-9826000/3703\) \(-8981330279907328\) \([2]\) \(1351680\) \(1.7710\) \(\Gamma_0(N)\)-optimal
236992.r1 236992r2 \([0, 1, 0, -1033313, -404606081]\) \(12576878500/1127\) \(10933793384235008\) \([2]\) \(2703360\) \(2.1176\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.r

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.