Elliptic curve isogeny class with Cremona label 202800im (LMFDB label 202800.kf)

• Label: 202800im
• Number of curves: $4$
• Conductor: $202800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 202800im have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 202800.2.a.im

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 202800im

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
202800.kf3	202800im1	\([0, 1, 0, -470383, -124033012]\)	\(9538484224/26325\)	\(31766436731250000\)	\([2]\)	\(3096576\)	\(2.0394\)	\(\Gamma_0(N)\)-optimal
202800.kf2	202800im2	\([0, 1, 0, -660508, -14521012]\)	\(1650587344/950625\)	\(18353941222500000000\)	\([2, 2]\)	\(6193152\)	\(2.3859\)
202800.kf1	202800im3	\([0, 1, 0, -6998008, 7096153988]\)	\(490757540836/2142075\)	\(165430190218800000000\)	\([2]\)	\(12386304\)	\(2.7325\)
202800.kf4	202800im4	\([0, 1, 0, 2634992, -113386012]\)	\(26198797244/15234375\)	\(-1176534693750000000000\)	\([2]\)	\(12386304\)	\(2.7325\)