Elliptic curve isogeny class with Cremona label 187200ck (LMFDB label 187200.o)

• Label: 187200ck
• Number of curves: $4$
• Conductor: $187200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 187200ck have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 187200ck do not have complex multiplication.

Modular form 187200.2.a.ck

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 187200ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
187200.o3	187200ck1	\([0, 0, 0, -100200, 12179000]\)	\(9538484224/26325\)	\(307054800000000\)	\([2]\)	\(1179648\)	\(1.6528\)	\(\Gamma_0(N)\)-optimal
187200.o2	187200ck2	\([0, 0, 0, -140700, 1406000]\)	\(1650587344/950625\)	\(177409440000000000\)	\([2, 2]\)	\(2359296\)	\(1.9993\)
187200.o4	187200ck3	\([0, 0, 0, 561300, 11234000]\)	\(26198797244/15234375\)	\(-11372400000000000000\)	\([2]\)	\(4718592\)	\(2.3459\)
187200.o1	187200ck4	\([0, 0, 0, -1490700, -697894000]\)	\(490757540836/2142075\)	\(1599050419200000000\)	\([2]\)	\(4718592\)	\(2.3459\)