Elliptic curve isogeny class with Cremona label 20280s (LMFDB label 20280.n)

• Label: 20280s
• Number of curves: $4$
• Conductor: $20280$
• CM: no
• Rank: $1$

Elliptic curves in class 20280s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20280.n4	20280s1	\([0, -1, 0, 14140, 452100]\)	\(253012016/219375\)	\(-271073593440000\)	\([4]\)	\(64512\)	\(1.4570\)	\(\Gamma_0(N)\)-optimal
20280.n3	20280s2	\([0, -1, 0, -70360, 4068700]\)	\(7793764996/3080025\)	\(15223493007590400\)	\([2, 2]\)	\(129024\)	\(1.8036\)
20280.n2	20280s3	\([0, -1, 0, -509760, -137066580]\)	\(1481943889298/34543665\)	\(341474658539489280\)	\([2]\)	\(258048\)	\(2.1501\)
20280.n1	20280s4	\([0, -1, 0, -982960, 375314380]\)	\(10625310339698/3855735\)	\(38115115826411520\)	\([2]\)	\(258048\)	\(2.1501\)

Rank

The elliptic curves in class 20280s have rank \(1\).

Complex multiplication

The elliptic curves in class 20280s do not have complex multiplication.

Modular form 20280.2.a.s

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.