Elliptic curve isogeny class with Cremona label 4704bf (LMFDB label 4704.t)

• Label: 4704bf
• Number of curves: $4$
• Conductor: $4704$
• CM: no
• Rank: $0$

Elliptic curves in class 4704bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4704.t3	4704bf1	\([0, 1, 0, -114, 216]\)	\(21952/9\)	\(67765824\)	\([2, 2]\)	\(1152\)	\(0.20016\)	\(\Gamma_0(N)\)-optimal
4704.t2	4704bf2	\([0, 1, 0, -849, -9633]\)	\(140608/3\)	\(1445670912\)	\([2]\)	\(2304\)	\(0.54673\)
4704.t1	4704bf3	\([0, 1, 0, -1584, 23736]\)	\(7301384/3\)	\(180708864\)	\([2]\)	\(2304\)	\(0.54673\)
4704.t4	4704bf4	\([0, 1, 0, 376, 1980]\)	\(97336/81\)	\(-4879139328\)	\([2]\)	\(2304\)	\(0.54673\)

Rank

The elliptic curves in class 4704bf have rank \(0\).

Complex multiplication

The elliptic curves in class 4704bf do not have complex multiplication.

Modular form 4704.2.a.bf

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.