Elliptic curve isogeny class with Cremona label 57200bj (LMFDB label 57200.bf)

• Label: 57200bj
• Number of curves: $4$
• Conductor: $57200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 57200bj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 57200bj do not have complex multiplication.

Modular form 57200.2.a.bj

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 57200bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57200.bf4	57200bj1	\([0, 0, 0, -23018675, -42853700750]\)	\(-21075830718885163521/199306463150080\)	\(-12755613641605120000000\)	\([2]\)	\(3870720\)	\(3.0629\)	\(\Gamma_0(N)\)-optimal
57200.bf3	57200bj2	\([0, 0, 0, -369130675, -2729721156750]\)	\(86912881496074271306241/7664481510400\)	\(490526816665600000000\)	\([2, 2]\)	\(7741440\)	\(3.4095\)
57200.bf2	57200bj3	\([0, 0, 0, -369962675, -2716797700750]\)	\(87501897507774086005761/815991377947460000\)	\(52223448188637440000000000\)	\([2]\)	\(15482880\)	\(3.7561\)
57200.bf1	57200bj4	\([0, 0, 0, -5906090675, -174702161796750]\)	\(355995140004443961140387841/2768480\)	\(177182720000000\)	\([2]\)	\(15482880\)	\(3.7561\)