Elliptic curve isogeny class with LMFDB label 768.b (Cremona label 768a)

• Label: 768.b
• Number of curves: $2$
• Conductor: $768$
• CM: no
• Rank: $1$

Elliptic curves in class 768.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
768.b1	768a1	\([0, -1, 0, -23, 51]\)	\(2744000/9\)	\(4608\)	\([2]\)	\(64\)	\(-0.43171\)	\(\Gamma_0(N)\)-optimal
768.b2	768a2	\([0, -1, 0, -13, 85]\)	\(-8000/81\)	\(-2654208\)	\([2]\)	\(128\)	\(-0.085141\)

Rank

The elliptic curves in class 768.b have rank \(1\).

Complex multiplication

The elliptic curves in class 768.b do not have complex multiplication.

Modular form 768.2.a.b

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.