Elliptic curve isogeny class with Cremona label 16800ba (LMFDB label 16800.bd)

• Label: 16800ba
• Number of curves: $2$
• Conductor: $16800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 16800ba 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 16800.2.a.ba

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 16800ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16800.bd2	16800ba1	\([0, 1, 0, 2, 308]\)	\(64/5103\)	\(-40824000\)	\([2]\)	\(4608\)	\(0.13929\)	\(\Gamma_0(N)\)-optimal
16800.bd1	16800ba2	\([0, 1, 0, -673, 6383]\)	\(65939264/1323\)	\(677376000\)	\([2]\)	\(9216\)	\(0.48586\)