Elliptic curve isogeny class with Cremona label 28440k (LMFDB label 28440.k)

• Label: 28440k
• Number of curves: $2$
• Conductor: $28440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 28440k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28440k do not have complex multiplication.

Modular form 28440.2.a.k

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 28440k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28440.k2	28440k1	\([0, 0, 0, 177, 178]\)	\(3286064/1975\)	\(-368582400\)	\([2]\)	\(7680\)	\(0.33304\)	\(\Gamma_0(N)\)-optimal
28440.k1	28440k2	\([0, 0, 0, -723, 1438]\)	\(55990084/31205\)	\(23294407680\)	\([2]\)	\(15360\)	\(0.67961\)