Elliptic curve isogeny class with Cremona label 128d (LMFDB label 128.d)

• Label: 128d
• Number of curves: $2$
• Conductor: $128$
• CM: no
• Rank: $0$

Elliptic curves in class 128d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
128.d2	128d1	\([0, -1, 0, 3, 5]\)	\(128\)	\(-16384\)	\([2]\)	\(8\)	\(-0.50986\)	\(\Gamma_0(N)\)-optimal
128.d1	128d2	\([0, -1, 0, -2, 2]\)	\(10976\)	\(128\)	\([2]\)	\(16\)	\(-0.85643\)

Rank

The elliptic curves in class 128d have rank \(0\).

Complex multiplication

The elliptic curves in class 128d do not have complex multiplication.

Modular form 128.2.a.d

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.