Elliptic curve isogeny class with Cremona label 499800fo (LMFDB label 499800.fo)

• Label: 499800fo
• Number of curves: $4$
• Conductor: $499800$
• CM: no
• Rank: $1$

Elliptic curves in class 499800fo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
499800.fo3	499800fo1	\([0, 1, 0, -146183, -21560862]\)	\(11745974272/357\)	\(10500173250000\)	\([2]\)	\(1966080\)	\(1.5964\)	\(\Gamma_0(N)\)-optimal^*
499800.fo2	499800fo2	\([0, 1, 0, -152308, -19662112]\)	\(830321872/127449\)	\(59976989604000000\)	\([2, 2]\)	\(3932160\)	\(1.9430\)	\(\Gamma_0(N)\)-optimal^*
499800.fo1	499800fo3	\([0, 1, 0, -666808, 190253888]\)	\(17418812548/1753941\)	\(3301590475344000000\)	\([2]\)	\(7864320\)	\(2.2895\)	\(\Gamma_0(N)\)-optimal^*
499800.fo4	499800fo4	\([0, 1, 0, 264192, -107960112]\)	\(1083360092/3306177\)	\(-6223494685968000000\)	\([2]\)	\(7864320\)	\(2.2895\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 499800fo1.

Rank

The elliptic curves in class 499800fo have rank \(1\).

Complex multiplication

The elliptic curves in class 499800fo do not have complex multiplication.

Modular form 499800.2.a.fo

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.