Elliptic curve isogeny class with Cremona label 158400ne (LMFDB label 158400.ol)

• Label: 158400ne
• Number of curves: $4$
• Conductor: $158400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 158400ne have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158400ne do not have complex multiplication.

Modular form 158400.2.a.ne

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 158400ne

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.ol4	158400ne1	\([0, 0, 0, -1170975, 387258500]\)	\(243578556889408/52089208083\)	\(37973032692507000000\)	\([2]\)	\(3932160\)	\(2.4712\)	\(\Gamma_0(N)\)-optimal
158400.ol2	158400ne2	\([0, 0, 0, -17642100, 28519940000]\)	\(13015685560572352/864536409\)	\(40335810698304000000\)	\([2, 2]\)	\(7864320\)	\(2.8178\)
158400.ol1	158400ne3	\([0, 0, 0, -282269100, 1825337270000]\)	\(6663712298552914184/29403\)	\(10974610944000000\)	\([2]\)	\(15728640\)	\(3.1644\)
158400.ol3	158400ne4	\([0, 0, 0, -16553100, 32194226000]\)	\(-1343891598641864/421900912521\)	\(-157473671796638208000000\)	\([2]\)	\(15728640\)	\(3.1644\)