Elliptic curve isogeny class with Cremona label 119658co (LMFDB label 119658.ci)

• Label: 119658co
• Number of curves: $4$
• Conductor: $119658$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 119658co have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 119658co do not have complex multiplication.

Modular form 119658.2.a.co

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 119658co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119658.ci4	119658co1	\([1, 1, 1, -75363, -2952447]\)	\(402355893390625/201513996288\)	\(23707920149286912\)	\([2]\)	\(995328\)	\(1.8348\)	\(\Gamma_0(N)\)-optimal
119658.ci3	119658co2	\([1, 1, 1, -655523, 201960065]\)	\(264788619837198625/3058196150592\)	\(359793718920998208\)	\([2]\)	\(1990656\)	\(2.1814\)
119658.ci2	119658co3	\([1, 1, 1, -3309363, 2315747937]\)	\(34069730739753390625/1354703543952\)	\(159379517242408848\)	\([2]\)	\(2985984\)	\(2.3841\)
119658.ci1	119658co4	\([1, 1, 1, -52949303, 148277027513]\)	\(139545621883503188502625/220644468\)	\(25958601015732\)	\([2]\)	\(5971968\)	\(2.7307\)