Elliptic Curve Isogeny Class with Cremona label 14400dp (LMFDB label 14400.cz)

• Label: 14400dp
• Number of curves: 8
• Conductor: 14400
• CM: no
• Rank: 1

Elliptic curves in class 14400dp

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
14400.cz7	14400dp1	[0, 0, 0, -300, 322000]	[2]	24576	\(\Gamma_0(N)\)-optimal
14400.cz6	14400dp2	[0, 0, 0, -72300, 7378000]	[2, 2]	49152
14400.cz5	14400dp3	[0, 0, 0, -144300, -9758000]	[2, 2]	98304
14400.cz4	14400dp4	[0, 0, 0, -1152300, 476098000]	[2]	98304
14400.cz2	14400dp5	[0, 0, 0, -1944300, -1042958000]	[2, 2]	196608
14400.cz8	14400dp6	[0, 0, 0, 503700, -73262000]	[2]	196608
14400.cz1	14400dp7	[0, 0, 0, -31104300, -66769598000]	[2]	393216
14400.cz3	14400dp8	[0, 0, 0, -1584300, -1441118000]	[2]	393216

Rank

The elliptic curves in class 14400dp have rank \(1\).

Modular form 14400.2.a.cz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.