Elliptic curve isogeny class with LMFDB label 16800.bm (Cremona label 16800bt)

• Label: 16800.bm
• Number of curves: $4$
• Conductor: $16800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 16800.bm have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 16800.bm do not have complex multiplication.

Modular form 16800.2.a.bm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 16800.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16800.bm1	16800bt3	\([0, 1, 0, -1639408, 807355688]\)	\(60910917333827912/3255076125\)	\(26040609000000000\)	\([4]\)	\(221184\)	\(2.2173\)
16800.bm2	16800bt2	\([0, 1, 0, -530033, -138659937]\)	\(257307998572864/19456203375\)	\(1245197016000000000\)	\([2]\)	\(221184\)	\(2.2173\)
16800.bm3	16800bt1	\([0, 1, 0, -108158, 11105688]\)	\(139927692143296/27348890625\)	\(27348890625000000\)	\([2, 2]\)	\(110592\)	\(1.8707\)	\(\Gamma_0(N)\)-optimal
16800.bm4	16800bt4	\([0, 1, 0, 222592, 66010188]\)	\(152461584507448/322998046875\)	\(-2583984375000000000\)	\([2]\)	\(221184\)	\(2.2173\)