Elliptic curve isogeny class with LMFDB label 162288.fc (Cremona label 162288ci)

• Label: 162288.fc
• Number of curves: $4$
• Conductor: $162288$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 162288.fc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162288.fc do not have complex multiplication.

Modular form 162288.2.a.fc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 162288.fc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162288.fc1	162288ci4	\([0, 0, 0, -1742979, -885560830]\)	\(1666957239793/301806\)	\(106023853729898496\)	\([2]\)	\(2359296\)	\(2.2704\)
162288.fc2	162288ci3	\([0, 0, 0, -755139, 244330562]\)	\(135559106353/5037138\)	\(1769536664378155008\)	\([2]\)	\(2359296\)	\(2.2704\)
162288.fc3	162288ci2	\([0, 0, 0, -120099, -10828510]\)	\(545338513/171396\)	\(60211077426855936\)	\([2, 2]\)	\(1179648\)	\(1.9238\)
162288.fc4	162288ci1	\([0, 0, 0, 21021, -1147678]\)	\(2924207/3312\)	\(-1163499080712192\)	\([2]\)	\(589824\)	\(1.5773\)	\(\Gamma_0(N)\)-optimal