Elliptic curve isogeny class with Cremona label 183150by (LMFDB label 183150.fk)

• Label: 183150by
• Number of curves: $4$
• Conductor: $183150$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 183150by have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 183150by do not have complex multiplication.

Modular form 183150.2.a.by

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 183150by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
183150.fk4	183150by1	\([1, -1, 1, -346055, -28655553]\)	\(402355893390625/201513996288\)	\(2295370363968000000\)	\([2]\)	\(3981312\)	\(2.2159\)	\(\Gamma_0(N)\)-optimal
183150.fk3	183150by2	\([1, -1, 1, -3010055, 1990656447]\)	\(264788619837198625/3058196150592\)	\(34834765527837000000\)	\([2]\)	\(7962624\)	\(2.5625\)
183150.fk2	183150by3	\([1, -1, 1, -15196055, 22803516447]\)	\(34069730739753390625/1354703543952\)	\(15430920055328250000\)	\([2]\)	\(11943936\)	\(2.7652\)
183150.fk1	183150by4	\([1, -1, 1, -243134555, 1459271943447]\)	\(139545621883503188502625/220644468\)	\(2513278393312500\)	\([2]\)	\(23887872\)	\(3.1118\)