Elliptic curve isogeny class with Cremona label 28800dj (LMFDB label 28800.k)

• Label: 28800dj
• Number of curves: $2$
• Conductor: $28800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 28800dj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28800dj do not have complex multiplication.

Modular form 28800.2.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 28800dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28800.k2	28800dj1	\([0, 0, 0, 150, 2500]\)	\(128\)	\(-2916000000\)	\([2]\)	\(12288\)	\(0.49760\)	\(\Gamma_0(N)\)-optimal
28800.k1	28800dj2	\([0, 0, 0, -2100, 34000]\)	\(10976\)	\(93312000000\)	\([2]\)	\(24576\)	\(0.84417\)