Elliptic curve isogeny class with Cremona label 84525by (LMFDB label 84525.da)

• Label: 84525by
• Number of curves: $4$
• Conductor: $84525$
• CM: no
• Rank: $1$

Elliptic curves in class 84525by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84525.da4	84525by1	\([1, 0, 1, -283001, -15254977]\)	\(1363569097969/734582625\)	\(1350357988259765625\)	\([2]\)	\(1216512\)	\(2.1700\)	\(\Gamma_0(N)\)-optimal
84525.da2	84525by2	\([1, 0, 1, -3523126, -2542552477]\)	\(2630872462131649/3645140625\)	\(6700736709228515625\)	\([2, 2]\)	\(2433024\)	\(2.5166\)
84525.da3	84525by3	\([1, 0, 1, -2537001, -3996100727]\)	\(-982374577874929/3183837890625\)	\(-5852739749908447265625\)	\([2]\)	\(4866048\)	\(2.8632\)
84525.da1	84525by4	\([1, 0, 1, -56351251, -162823083727]\)	\(10765299591712341649/20708625\)	\(38067953478515625\)	\([2]\)	\(4866048\)	\(2.8632\)

Rank

The elliptic curves in class 84525by have rank \(1\).

Complex multiplication

The elliptic curves in class 84525by do not have complex multiplication.

Modular form 84525.2.a.by

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.