Elliptic curve isogeny class with Cremona label 16758bc (LMFDB label 16758.bg)

• Label: 16758bc
• Number of curves: $3$
• Conductor: $16758$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 16758bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 16758bc do not have complex multiplication.

Modular form 16758.2.a.bc

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 16758bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16758.bg2	16758bc1	\([1, -1, 1, -6845, 219741]\)	\(-413493625/152\)	\(-13036450392\)	\([]\)	\(22680\)	\(0.90882\)	\(\Gamma_0(N)\)-optimal
16758.bg3	16758bc2	\([1, -1, 1, 4180, 827439]\)	\(94196375/3511808\)	\(-301194149856768\)	\([]\)	\(68040\)	\(1.4581\)
16758.bg1	16758bc3	\([1, -1, 1, -37715, -22667277]\)	\(-69173457625/2550136832\)	\(-218715344099868672\)	\([]\)	\(204120\)	\(2.0074\)