Elliptic curve isogeny class with Cremona label 382200gg (LMFDB label 382200.gg)

• Label: 382200gg
• Number of curves: $2$
• Conductor: $382200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 382200gg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 382200gg do not have complex multiplication.

Modular form 382200.2.a.gg

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 382200gg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
382200.gg2	382200gg1	\([0, 1, 0, -12646083, -17773119162]\)	\(-7604375980288000/236743082667\)	\(-6963146733172470750000\)	\([2]\)	\(26542080\)	\(2.9680\)	\(\Gamma_0(N)\)-optimal
382200.gg1	382200gg2	\([0, 1, 0, -203825708, -1120114836912]\)	\(1989996724085074000/1843096437\)	\(867353810866452000000\)	\([2]\)	\(53084160\)	\(3.3146\)