Elliptic curve isogeny class with Cremona label 36800cp (LMFDB label 36800.ck)

• Label: 36800cp
• Number of curves: $2$
• Conductor: $36800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 36800cp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 36800cp do not have complex multiplication.

Modular form 36800.2.a.cp

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 36800cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36800.ck2	36800cp1	\([0, 0, 0, 500, -6000]\)	\(13500/23\)	\(-23552000000\)	\([2]\)	\(27648\)	\(0.67517\)	\(\Gamma_0(N)\)-optimal
36800.ck1	36800cp2	\([0, 0, 0, -3500, -62000]\)	\(2315250/529\)	\(1083392000000\)	\([2]\)	\(55296\)	\(1.0217\)