Elliptic curve isogeny class with LMFDB label 18150.bi (Cremona label 18150y)

• Label: 18150.bi
• Number of curves: $4$
• Conductor: $18150$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 18150.bi have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 18150.bi do not have complex multiplication.

Modular form 18150.2.a.bi

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 18150.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
18150.bi1	18150y3	\([1, 0, 1, -12594651, -13157606552]\)	\(7981893677157049/1917731420550\)	\(53084034267515289843750\)	\([2]\)	\(1843200\)	\(3.0717\)
18150.bi2	18150y2	\([1, 0, 1, -4275901, 3230330948]\)	\(312341975961049/17862322500\)	\(494440529850351562500\)	\([2, 2]\)	\(921600\)	\(2.7251\)
18150.bi3	18150y1	\([1, 0, 1, -4215401, 3330881948]\)	\(299270638153369/1069200\)	\(29596140956250000\)	\([2]\)	\(460800\)	\(2.3785\)	\(\Gamma_0(N)\)-optimal
18150.bi4	18150y4	\([1, 0, 1, 3074849, 13183246448]\)	\(116149984977671/2779502343750\)	\(-76938405493688964843750\)	\([2]\)	\(1843200\)	\(3.0717\)