Elliptic curve isogeny class with Cremona label 48400cg (LMFDB label 48400.dh)

• Label: 48400cg
• Number of curves: $2$
• Conductor: $48400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 48400cg have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48400cg do not have complex multiplication.

Modular form 48400.2.a.cg

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 48400cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48400.dh2	48400cg1	\([0, -1, 0, -12008, 510512]\)	\(-24729001\)	\(-7744000000\)	\([]\)	\(53760\)	\(0.97991\)	\(\Gamma_0(N)\)-optimal
48400.dh1	48400cg2	\([0, -1, 0, -122008, -64081488]\)	\(-121\)	\(-1659995174464000000\)	\([]\)	\(591360\)	\(2.1789\)