Elliptic curve isogeny class with Cremona label 14400ed (LMFDB label 14400.ex)

• Label: 14400ed
• Number of curves: $4$
• Conductor: $14400$
• CM: no
• Rank: $1$

Rank

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

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 14400ed do not have complex multiplication.

Modular form 14400.2.a.ed

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 14400ed

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14400.ex4	14400ed1	\([0, 0, 0, 825, -97000]\)	\(85184/5625\)	\(-4100625000000\)	\([2]\)	\(24576\)	\(1.0998\)	\(\Gamma_0(N)\)-optimal
14400.ex3	14400ed2	\([0, 0, 0, -27300, -1672000]\)	\(48228544/2025\)	\(94478400000000\)	\([2, 2]\)	\(49152\)	\(1.4463\)
14400.ex1	14400ed3	\([0, 0, 0, -432300, -109402000]\)	\(23937672968/45\)	\(16796160000000\)	\([2]\)	\(98304\)	\(1.7929\)
14400.ex2	14400ed4	\([0, 0, 0, -72300, 5258000]\)	\(111980168/32805\)	\(12244400640000000\)	\([2]\)	\(98304\)	\(1.7929\)