Elliptic curve isogeny class with Cremona label 308550fk (LMFDB label 308550.fk)

• Label: 308550fk
• Number of curves: $4$
• Conductor: $308550$
• CM: no
• Rank: $1$

Elliptic curves in class 308550fk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
308550.fk3	308550fk1	\([1, 1, 1, -6249713, -15194665969]\)	\(-975276594443809/3037581803520\)	\(-84082210272276480000000\)	\([2]\)	\(39813120\)	\(3.0854\)	\(\Gamma_0(N)\)-optimal
308550.fk2	308550fk2	\([1, 1, 1, -137897713, -622618537969]\)	\(10476561483361670689/13992628953600\)	\(387324933463571400000000\)	\([2]\)	\(79626240\)	\(3.4320\)
308550.fk4	308550fk3	\([1, 1, 1, 54734287, 352050982031]\)	\(655127711084516831/2313151512408000\)	\(-64029515726141076375000000\)	\([2]\)	\(119439360\)	\(3.6347\)
308550.fk1	308550fk4	\([1, 1, 1, -539738713, 4200669184031]\)	\(628200507126935410849/88124751829125000\)	\(2439349585549320533203125000\)	\([2]\)	\(238878720\)	\(3.9813\)

Rank

The elliptic curves in class 308550fk have rank \(1\).

Complex multiplication

The elliptic curves in class 308550fk do not have complex multiplication.

Modular form 308550.2.a.fk

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.