Elliptic curve isogeny class with Cremona label 288834y (LMFDB label 288834.y)

• Label: 288834y
• Number of curves: $4$
• Conductor: $288834$
• CM: no
• Rank: $1$

Elliptic curves in class 288834y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
288834.y3	288834y1	\([1, 0, 1, -29900, 1932554]\)	\(19968681097/628992\)	\(93113389893888\)	\([2]\)	\(1182720\)	\(1.4552\)	\(\Gamma_0(N)\)-optimal
288834.y2	288834y2	\([1, 0, 1, -72220, -4770934]\)	\(281397674377/96589584\)	\(14298724935580176\)	\([2, 2]\)	\(2365440\)	\(1.8018\)
288834.y4	288834y3	\([1, 0, 1, 213440, -33108406]\)	\(7264187703863/7406095788\)	\(-1096367973995735532\)	\([2]\)	\(4730880\)	\(2.1484\)
288834.y1	288834y4	\([1, 0, 1, -1035000, -405287414]\)	\(828279937799497/193444524\)	\(28636732082521836\)	\([2]\)	\(4730880\)	\(2.1484\)

Rank

The elliptic curves in class 288834y have rank \(1\).

Complex multiplication

The elliptic curves in class 288834y do not have complex multiplication.

Modular form 288834.2.a.y

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.