Elliptic curve isogeny class with Cremona label 76664b (LMFDB label 76664.b)

• Label: 76664b
• Number of curves: $4$
• Conductor: $76664$
• CM: no
• Rank: $1$

Elliptic curves in class 76664b

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
76664.b4	76664b1	[0, 0, 0, 1369, 101306]	[2]	103680	\(\Gamma_0(N)\)-optimal
76664.b3	76664b2	[0, 0, 0, -26011, 1519590]	[2, 2]	207360
76664.b2	76664b3	[0, 0, 0, -80771, -6990114]	[2]	414720
76664.b1	76664b4	[0, 0, 0, -409331, 100799470]	[2]	414720

Rank

The elliptic curves in class 76664b have rank \(1\).

Complex multiplication

The elliptic curves in class 76664b do not have complex multiplication.

Modular form 76664.2.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 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.