Elliptic curve isogeny class with Cremona label 218400dz (LMFDB label 218400.do)

• Label: 218400dz
• Number of curves: $4$
• Conductor: $218400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 218400dz have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 218400dz do not have complex multiplication.

Modular form 218400.2.a.dz

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.

Elliptic curves in class 218400dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
218400.do3	218400dz1	\([0, 1, 0, -9758, 169488]\)	\(102766285504/46580625\)	\(46580625000000\)	\([2, 2]\)	\(589824\)	\(1.3178\)	\(\Gamma_0(N)\)-optimal
218400.do1	218400dz2	\([0, 1, 0, -131633, 18328863]\)	\(3941317078336/2340975\)	\(149822400000000\)	\([2]\)	\(1179648\)	\(1.6644\)
218400.do4	218400dz3	\([0, 1, 0, 33992, 1306988]\)	\(542939080312/404852175\)	\(-3238817400000000\)	\([2]\)	\(1179648\)	\(1.6644\)
218400.do2	218400dz4	\([0, 1, 0, -78008, -8293512]\)	\(6562309703048/106640625\)	\(853125000000000\)	\([2]\)	\(1179648\)	\(1.6644\)