Elliptic curve isogeny class with LMFDB label 361998.cn (Cremona label 361998cn)

• Label: 361998.cn
• Number of curves: $6$
• Conductor: $361998$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 361998.cn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 361998.cn do not have complex multiplication.

Modular form 361998.2.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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 361998.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
361998.cn1	361998cn5	\([1, -1, 1, -20865996716, 1160135576072295]\)	\(285531136548675601769470657/17941034271597192\)	\(63129902409069798855119112\)	\([2]\)	\(566231040\)	\(4.4109\)
361998.cn2	361998cn3	\([1, -1, 1, -1306605956, 18054925839591]\)	\(70108386184777836280897/552468975892674624\)	\(1943996762068408238803020864\)	\([2, 2]\)	\(283115520\)	\(4.0643\)
361998.cn3	361998cn6	\([1, -1, 1, -445050716, 41508527204967]\)	\(-2770540998624539614657/209924951154647363208\)	\(-738672112153645155443250945288\)	\([2]\)	\(566231040\)	\(4.4109\)
361998.cn4	361998cn2	\([1, -1, 1, -137991236, -156765956889]\)	\(82582985847542515777/44772582831427584\)	\(157543246501941525923303424\)	\([2, 2]\)	\(141557760\)	\(3.7178\)
361998.cn5	361998cn1	\([1, -1, 1, -106841156, -424507124505]\)	\(38331145780597164097/55468445663232\)	\(195179247109865107095552\)	\([2]\)	\(70778880\)	\(3.3712\)	\(\Gamma_0(N)\)-optimal
361998.cn6	361998cn4	\([1, -1, 1, 532222204, -1233396826905]\)	\(4738217997934888496063/2928751705237796928\)	\(-10305526790323608961784966208\)	\([2]\)	\(283115520\)	\(4.0643\)