Elliptic curve isogeny class with LMFDB label 14400.bb (Cremona label 14400k)

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

Rank

The elliptic curves in class 14400.bb 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.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 14400.2.a.bb

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 14400.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14400.bb1	14400k4	\([0, 0, 0, -1838700, -959634000]\)	\(8527173507/200\)	\(16124313600000000\)	\([2]\)	\(221184\)	\(2.2220\)
14400.bb2	14400k3	\([0, 0, 0, -110700, -16146000]\)	\(-1860867/320\)	\(-25798901760000000\)	\([2]\)	\(110592\)	\(1.8754\)
14400.bb3	14400k2	\([0, 0, 0, -38700, 766000]\)	\(57960603/31250\)	\(3456000000000000\)	\([2]\)	\(73728\)	\(1.6727\)
14400.bb4	14400k1	\([0, 0, 0, 9300, 94000]\)	\(804357/500\)	\(-55296000000000\)	\([2]\)	\(36864\)	\(1.3261\)	\(\Gamma_0(N)\)-optimal