Elliptic curve isogeny class with Cremona label 14400bp (LMFDB label 14400.fd)

• Label: 14400bp
• Number of curves: $4$
• Conductor: $14400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 14400bp have rank \(0\).

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.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 14400.2.a.bp

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 14400bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14400.fd3	14400bp1	\([0, 0, 0, -1800, -27000]\)	\(55296/5\)	\(58320000000\)	\([2]\)	\(12288\)	\(0.80524\)	\(\Gamma_0(N)\)-optimal
14400.fd2	14400bp2	\([0, 0, 0, -6300, 162000]\)	\(148176/25\)	\(4665600000000\)	\([2, 2]\)	\(24576\)	\(1.1518\)
14400.fd1	14400bp3	\([0, 0, 0, -96300, 11502000]\)	\(132304644/5\)	\(3732480000000\)	\([2]\)	\(49152\)	\(1.4984\)
14400.fd4	14400bp4	\([0, 0, 0, 11700, 918000]\)	\(237276/625\)	\(-466560000000000\)	\([2]\)	\(49152\)	\(1.4984\)