Elliptic curve isogeny class with LMFDB label 54208.bi (Cremona label 54208bw)

• Label: 54208.bi
• Number of curves: $4$
• Conductor: $54208$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 54208.bi have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	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 54208.bi do not have complex multiplication.

Modular form 54208.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 54208.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54208.bi1	54208bw4	\([0, 0, 0, -39987596, -97327596784]\)	\(15226621995131793/2324168\)	\(1079353117572595712\)	\([2]\)	\(2211840\)	\(2.8658\)
54208.bi2	54208bw3	\([0, 0, 0, -4674956, 1494020880]\)	\(24331017010833/12004097336\)	\(5574751860991327207424\)	\([2]\)	\(2211840\)	\(2.8658\)
54208.bi3	54208bw2	\([0, 0, 0, -2506636, -1511270640]\)	\(3750606459153/45914176\)	\(21322730975719849984\)	\([2, 2]\)	\(1105920\)	\(2.5193\)
54208.bi4	54208bw1	\([0, 0, 0, -28556, -61098224]\)	\(-5545233/3469312\)	\(-1611162671128772608\)	\([2]\)	\(552960\)	\(2.1727\)	\(\Gamma_0(N)\)-optimal