Elliptic curve isogeny class with Cremona label 4680n (LMFDB label 4680.i)

• Label: 4680n
• Number of curves: $2$
• Conductor: $4680$
• CM: no
• Rank: $1$

Elliptic curves in class 4680n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4680.i2	4680n1	\([0, 0, 0, 6477, 212222]\)	\(40254822716/49359375\)	\(-36846576000000\)	\([2]\)	\(7680\)	\(1.2893\)	\(\Gamma_0(N)\)-optimal
4680.i1	4680n2	\([0, 0, 0, -38523, 2039222]\)	\(4234737878642/1247410125\)	\(1862373337344000\)	\([2]\)	\(15360\)	\(1.6358\)

Rank

The elliptic curves in class 4680n have rank \(1\).

Complex multiplication

The elliptic curves in class 4680n do not have complex multiplication.

Modular form 4680.2.a.n

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.