Elliptic curve isogeny class with LMFDB label 48400.cd (Cremona label 48400k)

• Label: 48400.cd
• Number of curves: $4$
• Conductor: $48400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 48400.cd have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	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 48400.cd do not have complex multiplication.

Modular form 48400.2.a.cd

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 48400.cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48400.cd1	48400k4	\([0, 0, 0, -323675, -70875750]\)	\(132304644/5\)	\(141724880000000\)	\([2]\)	\(245760\)	\(1.8015\)
48400.cd2	48400k2	\([0, 0, 0, -21175, -998250]\)	\(148176/25\)	\(177156100000000\)	\([2, 2]\)	\(122880\)	\(1.4549\)
48400.cd3	48400k1	\([0, 0, 0, -6050, 166375]\)	\(55296/5\)	\(2214451250000\)	\([2]\)	\(61440\)	\(1.1083\)	\(\Gamma_0(N)\)-optimal
48400.cd4	48400k3	\([0, 0, 0, 39325, -5656750]\)	\(237276/625\)	\(-17715610000000000\)	\([2]\)	\(245760\)	\(1.8015\)