Elliptic curve isogeny class with Cremona label 16170bf (LMFDB label 16170.bh)

• Label: 16170bf
• Number of curves: $4$
• Conductor: $16170$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 16170bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 16170bf do not have complex multiplication.

Modular form 16170.2.a.bf

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 16170bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16170.bh3	16170bf1	\([1, 0, 1, -42313, 3339788]\)	\(71210194441849/165580800\)	\(19480415539200\)	\([2]\)	\(73728\)	\(1.4306\)	\(\Gamma_0(N)\)-optimal
16170.bh2	16170bf2	\([1, 0, 1, -57993, 636556]\)	\(183337554283129/104587560000\)	\(12304621846440000\)	\([2, 2]\)	\(147456\)	\(1.7772\)
16170.bh1	16170bf3	\([1, 0, 1, -596993, -176802244]\)	\(200005594092187129/1027287538200\)	\(120859351581691800\)	\([2]\)	\(294912\)	\(2.1238\)
16170.bh4	16170bf4	\([1, 0, 1, 230127, 5131228]\)	\(11456208593737991/6725709375000\)	\(-791272982259375000\)	\([2]\)	\(294912\)	\(2.1238\)