Elliptic curve isogeny class with LMFDB label 4800.bz (Cremona label 4800cd)

• Label: 4800.bz
• Number of curves: $8$
• Conductor: $4800$
• CM: no
• Rank: $1$

Elliptic curves in class 4800.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4800.bz1	4800cd7	\([0, 1, 0, -3456033, 2471796063]\)	\(1114544804970241/405\)	\(1658880000000\)	\([2]\)	\(49152\)	\(2.1353\)
4800.bz2	4800cd5	\([0, 1, 0, -216033, 38556063]\)	\(272223782641/164025\)	\(671846400000000\)	\([2, 2]\)	\(24576\)	\(1.7887\)
4800.bz3	4800cd8	\([0, 1, 0, -176033, 53316063]\)	\(-147281603041/215233605\)	\(-881596846080000000\)	\([2]\)	\(49152\)	\(2.1353\)
4800.bz4	4800cd3	\([0, 1, 0, -128033, -17675937]\)	\(56667352321/15\)	\(61440000000\)	\([2]\)	\(12288\)	\(1.4422\)
4800.bz5	4800cd4	\([0, 1, 0, -16033, 356063]\)	\(111284641/50625\)	\(207360000000000\)	\([2, 2]\)	\(12288\)	\(1.4422\)
4800.bz6	4800cd2	\([0, 1, 0, -8033, -275937]\)	\(13997521/225\)	\(921600000000\)	\([2, 2]\)	\(6144\)	\(1.0956\)
4800.bz7	4800cd1	\([0, 1, 0, -33, -11937]\)	\(-1/15\)	\(-61440000000\)	\([2]\)	\(3072\)	\(0.74901\)	\(\Gamma_0(N)\)-optimal
4800.bz8	4800cd6	\([0, 1, 0, 55967, 2732063]\)	\(4733169839/3515625\)	\(-14400000000000000\)	\([2]\)	\(24576\)	\(1.7887\)

Rank

The elliptic curves in class 4800.bz have rank \(1\).

Complex multiplication

The elliptic curves in class 4800.bz do not have complex multiplication.

Modular form 4800.2.a.bz

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.