Elliptic curve isogeny class with Cremona label 162288fp (LMFDB label 162288.es)

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

Rank

The elliptic curves in class 162288fp 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
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 162288.2.a.fp

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 162288fp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162288.es3	162288fp1	\([0, 0, 0, -91434, 10641575]\)	\(61604313088/621\)	\(852172178256\)	\([2]\)	\(442368\)	\(1.4482\)	\(\Gamma_0(N)\)-optimal
162288.es2	162288fp2	\([0, 0, 0, -93639, 10101350]\)	\(4135597648/385641\)	\(8467182763151616\)	\([2, 2]\)	\(884736\)	\(1.7948\)
162288.es4	162288fp3	\([0, 0, 0, 109221, 47873882]\)	\(1640689628/12223143\)	\(-1073491519015222272\)	\([2]\)	\(1769472\)	\(2.1413\)
162288.es1	162288fp4	\([0, 0, 0, -331779, -62245582]\)	\(45989074372/7555707\)	\(663576249141808128\)	\([2]\)	\(1769472\)	\(2.1413\)