Elliptic curve isogeny class with Cremona label 52800dj (LMFDB label 52800.fg)

• Label: 52800dj
• Number of curves: $2$
• Conductor: $52800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 52800dj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 52800dj do not have complex multiplication.

Modular form 52800.2.a.dj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 52800dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52800.fg1	52800dj1	\([0, 1, 0, -101333, -10268037]\)	\(57537462272/10673289\)	\(21346578000000000\)	\([2]\)	\(368640\)	\(1.8515\)	\(\Gamma_0(N)\)-optimal
52800.fg2	52800dj2	\([0, 1, 0, 201167, -59575537]\)	\(28134667888/64304361\)	\(-2057739552000000000\)	\([2]\)	\(737280\)	\(2.1981\)