Elliptic curve isogeny class with Cremona label 81733c (LMFDB label 81733.c)

• Label: 81733c
• Number of curves: $3$
• Conductor: $81733$
• CM: no
• Rank: $1$

Elliptic curves in class 81733c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81733.c3	81733c1	\([0, 1, 1, -7363, -243747]\)	\(4096000/37\)	\(398830967173\)	\([]\)	\(70380\)	\(1.0485\)	\(\Gamma_0(N)\)-optimal
81733.c2	81733c2	\([0, 1, 1, -51543, 4344346]\)	\(1404928000/50653\)	\(545999594059837\)	\([]\)	\(211140\)	\(1.5978\)
81733.c1	81733c3	\([0, 1, 1, -4138193, 3238764355]\)	\(727057727488000/37\)	\(398830967173\)	\([]\)	\(633420\)	\(2.1472\)

Rank

The elliptic curves in class 81733c have rank \(1\).

Complex multiplication

The elliptic curves in class 81733c do not have complex multiplication.

Modular form 81733.2.a.c

Isogeny 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.