Elliptic curve isogeny class with LMFDB label 202800.gb (Cremona label 202800br)

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

Rank

The elliptic curves in class 202800.gb 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 202800.2.a.gb

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 202800.gb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
202800.gb1	202800br4	\([0, 1, 0, -5849328008, -172191613152012]\)	\(71647584155243142409/10140000\)	\(3132405968640000000000\)	\([2]\)	\(123863040\)	\(3.9776\)
202800.gb2	202800br3	\([0, 1, 0, -419696008, -1841992672012]\)	\(26465989780414729/10571870144160\)	\(3265817469354418268160000000\)	\([2]\)	\(123863040\)	\(3.9776\)
202800.gb3	202800br2	\([0, 1, 0, -365616008, -2690075232012]\)	\(17496824387403529/6580454400\)	\(2032806177408614400000000\)	\([2, 2]\)	\(61931520\)	\(3.6310\)
202800.gb4	202800br1	\([0, 1, 0, -19504008, -54778464012]\)	\(-2656166199049/2658140160\)	\(-821141430243164160000000\)	\([2]\)	\(30965760\)	\(3.2845\)	\(\Gamma_0(N)\)-optimal