Elliptic curve isogeny class with LMFDB label 202800.gs (Cremona label 202800bx)

• Label: 202800.gs
• Number of curves: $4$
• Conductor: $202800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 202800.gs have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 202800.gs do not have complex multiplication.

Modular form 202800.2.a.gs

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 202800.gs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
202800.gs1	202800bx4	\([0, 1, 0, -80851008, 265552247988]\)	\(189208196468929/10860320250\)	\(3354924257637264000000000\)	\([2]\)	\(27869184\)	\(3.4602\)
202800.gs2	202800bx2	\([0, 1, 0, -13927008, -19921200012]\)	\(967068262369/4928040\)	\(1522349300759040000000\)	\([2]\)	\(9289728\)	\(2.9109\)
202800.gs3	202800bx1	\([0, 1, 0, -407008, -641680012]\)	\(-24137569/561600\)	\(-173487099801600000000\)	\([2]\)	\(4644864\)	\(2.5643\)	\(\Gamma_0(N)\)-optimal
202800.gs4	202800bx3	\([0, 1, 0, 3648992, 16953247988]\)	\(17394111071/411937500\)	\(-127253992476000000000000\)	\([2]\)	\(13934592\)	\(3.1136\)