Elliptic curve isogeny class with Cremona label 54208bd (LMFDB label 54208.bk)

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

Rank

The elliptic curves in class 54208bd 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 54208bd do not have complex multiplication.

Modular form 54208.2.a.bd

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 54208bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54208.bk4	54208bd1	\([0, 0, 0, -28556, 61098224]\)	\(-5545233/3469312\)	\(-1611162671128772608\)	\([2]\)	\(552960\)	\(2.1727\)	\(\Gamma_0(N)\)-optimal
54208.bk3	54208bd2	\([0, 0, 0, -2506636, 1511270640]\)	\(3750606459153/45914176\)	\(21322730975719849984\)	\([2, 2]\)	\(1105920\)	\(2.5193\)
54208.bk2	54208bd3	\([0, 0, 0, -4674956, -1494020880]\)	\(24331017010833/12004097336\)	\(5574751860991327207424\)	\([2]\)	\(2211840\)	\(2.8658\)
54208.bk1	54208bd4	\([0, 0, 0, -39987596, 97327596784]\)	\(15226621995131793/2324168\)	\(1079353117572595712\)	\([2]\)	\(2211840\)	\(2.8658\)