Elliptic curve isogeny class with Cremona label 162288bu (LMFDB label 162288.dz)

• Label: 162288bu
• Number of curves: $4$
• Conductor: $162288$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 162288bu have rank \(1\).

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.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 162288.2.a.bu

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 162288bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162288.dz4	162288bu1	\([0, 0, 0, 32771445, -508544305094]\)	\(11079872671250375/324440155855872\)	\(-113975188129356089395249152\)	\([2]\)	\(44236800\)	\(3.6799\)	\(\Gamma_0(N)\)-optimal
162288.dz2	162288bu2	\([0, 0, 0, -790240395, -8146587987398]\)	\(155355156733986861625/8291568305839392\)	\(2912811624850990288234217472\)	\([2]\)	\(88473600\)	\(4.0265\)
162288.dz3	162288bu3	\([0, 0, 0, -295861755, 13971941514538]\)	\(-8152944444844179625/235342826399858688\)	\(-82675471669216356834956279808\)	\([2]\)	\(132710400\)	\(4.2292\)
162288.dz1	162288bu4	\([0, 0, 0, -10700357115, 423969404771626]\)	\(385693937170561837203625/2159357734550274048\)	\(758578121702296308055768301568\)	\([2]\)	\(265420800\)	\(4.5758\)