Elliptic curve isogeny class with Cremona label 54208bx (LMFDB label 54208.bj)

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

Rank

The elliptic curves in class 54208bx 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
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 54208.2.a.bx

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 54208bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54208.bj4	54208bx1	\([0, 0, 0, 484, 21296]\)	\(432/7\)	\(-203176787968\)	\([2]\)	\(40960\)	\(0.85034\)	\(\Gamma_0(N)\)-optimal
54208.bj3	54208bx2	\([0, 0, 0, -9196, 319440]\)	\(740772/49\)	\(5688950063104\)	\([2, 2]\)	\(81920\)	\(1.1969\)
54208.bj2	54208bx3	\([0, 0, 0, -28556, -1469424]\)	\(11090466/2401\)	\(557517106184192\)	\([2]\)	\(163840\)	\(1.5435\)
54208.bj1	54208bx4	\([0, 0, 0, -144716, 21189520]\)	\(1443468546/7\)	\(1625414303744\)	\([2]\)	\(163840\)	\(1.5435\)