Elliptic curve isogeny class with Cremona label 462f (LMFDB label 462.g)

• Label: 462f
• Number of curves: $4$
• Conductor: $462$
• CM: no
• Rank: $0$

Elliptic curves in class 462f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
462.g4	462f1	\([1, 0, 0, -97, 1337]\)	\(-100999381393/723148272\)	\(-723148272\)	\([4]\)	\(192\)	\(0.38308\)	\(\Gamma_0(N)\)-optimal
462.g3	462f2	\([1, 0, 0, -2517, 48285]\)	\(1763535241378513/4612311396\)	\(4612311396\)	\([2, 2]\)	\(384\)	\(0.72966\)
462.g2	462f3	\([1, 0, 0, -3507, 6507]\)	\(4770223741048753/2740574865798\)	\(2740574865798\)	\([2]\)	\(768\)	\(1.0762\)
462.g1	462f4	\([1, 0, 0, -40247, 3104415]\)	\(7209828390823479793/49509306\)	\(49509306\)	\([2]\)	\(768\)	\(1.0762\)

Rank

The elliptic curves in class 462f have rank \(0\).

Complex multiplication

The elliptic curves in class 462f do not have complex multiplication.

Modular form 462.2.a.f

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.