Elliptic curve isogeny class with LMFDB label 218400.by (Cremona label 218400fb)

• Label: 218400.by
• Number of curves: $4$
• Conductor: $218400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 218400.by have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 218400.by do not have complex multiplication.

Modular form 218400.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 218400.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
218400.by1	218400fb4	\([0, -1, 0, -122008, -16360988]\)	\(25107427013768/2985255\)	\(23882040000000\)	\([2]\)	\(983040\)	\(1.5922\)
218400.by2	218400fb2	\([0, -1, 0, -47633, 3847137]\)	\(186756901696/8996715\)	\(575789760000000\)	\([2]\)	\(983040\)	\(1.5922\)
218400.by3	218400fb1	\([0, -1, 0, -8258, -208488]\)	\(62287505344/16769025\)	\(16769025000000\)	\([2, 2]\)	\(491520\)	\(1.2457\)	\(\Gamma_0(N)\)-optimal
218400.by4	218400fb3	\([0, -1, 0, 20992, -1378488]\)	\(127871714872/175573125\)	\(-1404585000000000\)	\([2]\)	\(983040\)	\(1.5922\)