Elliptic curve isogeny class with LMFDB label 212800.gg (Cremona label 212800cm)

• Label: 212800.gg
• Number of curves: $4$
• Conductor: $212800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 212800.gg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 212800.gg do not have complex multiplication.

Modular form 212800.2.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 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 212800.gg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212800.gg1	212800cm3	\([0, 0, 0, -9080300, 10531698000]\)	\(20214562937713929/665000\)	\(2723840000000000\)	\([2]\)	\(4423680\)	\(2.4624\)
212800.gg2	212800cm2	\([0, 0, 0, -568300, 164082000]\)	\(4955605568649/28302400\)	\(115926630400000000\)	\([2, 2]\)	\(2211840\)	\(2.1158\)
212800.gg3	212800cm4	\([0, 0, 0, -248300, 347762000]\)	\(-413327139849/12516028840\)	\(-51265654128640000000\)	\([2]\)	\(4423680\)	\(2.4624\)
212800.gg4	212800cm1	\([0, 0, 0, -56300, -782000]\)	\(4818245769/2723840\)	\(11156848640000000\)	\([2]\)	\(1105920\)	\(1.7692\)	\(\Gamma_0(N)\)-optimal