Elliptic curve isogeny class with LMFDB label 110110.cn (Cremona label 110110ch)

• Label: 110110.cn
• Number of curves: $3$
• Conductor: $110110$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 110110.cn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 110110.cn do not have complex multiplication.

Modular form 110110.2.a.cn

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 110110.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110110.cn1	110110ch3	\([1, 0, 0, -6110886900, 194995797894800]\)	\(-14245586655234650511684983641/1028175397808386133196800\)	\(-1821475435916822346512256204800\)	\([]\)	\(257191200\)	\(4.5561\)
110110.cn2	110110ch1	\([1, 0, 0, -69992150, -244395377500]\)	\(-21405018343206000779641/2177246093750000000\)	\(-3857124267089843750000000\)	\([]\)	\(28576800\)	\(3.4575\)	\(\Gamma_0(N)\)-optimal
110110.cn3	110110ch2	\([1, 0, 0, 431023475, 224201700625]\)	\(4998853083179567995470359/2905108466204672000000\)	\(-5146576859498014932992000000\)	\([]\)	\(85730400\)	\(4.0068\)