Elliptic curve isogeny class with Cremona label 286650dr (LMFDB label 286650.dr)

• Label: 286650dr
• Number of curves: $4$
• Conductor: $286650$
• CM: no
• Rank: $1$

Elliptic curves in class 286650dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
286650.dr4	286650dr1	\([1, -1, 0, -3180942, 3608293716]\)	\(-2656166199049/2658140160\)	\(-3562162040586240000000\)	\([2]\)	\(17694720\)	\(2.8311\)	\(\Gamma_0(N)\)-optimal
286650.dr3	286650dr2	\([1, -1, 0, -59628942, 177185893716]\)	\(17496824387403529/6580454400\)	\(8818438254771600000000\)	\([2, 2]\)	\(35389440\)	\(3.1777\)
286650.dr1	286650dr3	\([1, -1, 0, -953976942, 11341331977716]\)	\(71647584155243142409/10140000\)	\(13588569795937500000\)	\([2]\)	\(70778880\)	\(3.5242\)
286650.dr2	286650dr4	\([1, -1, 0, -68448942, 121328833716]\)	\(26465989780414729/10571870144160\)	\(14167317093442406302500000\)	\([2]\)	\(70778880\)	\(3.5242\)

Rank

The elliptic curves in class 286650dr have rank \(1\).

Complex multiplication

The elliptic curves in class 286650dr do not have complex multiplication.

Modular form 286650.2.a.dr

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.