Elliptic curve isogeny class with Cremona label 14400l (LMFDB label 14400.ey)

• Label: 14400l
• Number of curves: $4$
• Conductor: $14400$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Rank

The elliptic curves in class 14400l 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 14400l has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 14400.2.a.l

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 14400l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
14400.ey4	14400l1	\([0, 0, 0, 0, 1000]\)	\(0\)	\(-432000000\)	\([2]\)	\(4608\)	\(0.33588\)	\(\Gamma_0(N)\)-optimal	\(-3\)
14400.ey2	14400l2	\([0, 0, 0, -1500, 22000]\)	\(54000\)	\(6912000000\)	\([2]\)	\(9216\)	\(0.68245\)		\(-12\)
14400.ey3	14400l3	\([0, 0, 0, 0, -27000]\)	\(0\)	\(-314928000000\)	\([2]\)	\(13824\)	\(0.88518\)		\(-3\)
14400.ey1	14400l4	\([0, 0, 0, -13500, -594000]\)	\(54000\)	\(5038848000000\)	\([2]\)	\(27648\)	\(1.2318\)		\(-12\)