Elliptic curve isogeny class with LMFDB label 165165.u (Cremona label 165165n)

• Label: 165165.u
• Number of curves: $4$
• Conductor: $165165$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 165165.u have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 165165.u do not have complex multiplication.

Modular form 165165.2.a.u

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 165165.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
165165.u1	165165n4	\([1, 0, 0, -18211410, -17358387903]\)	\(377049455876971757881/144736610099956875\)	\(256409733725289701431875\)	\([2]\)	\(16220160\)	\(3.1909\)
165165.u2	165165n2	\([1, 0, 0, -8089155, 8661880800]\)	\(33042817838684613961/823326411132225\)	\(1458572960231815653225\)	\([2, 2]\)	\(8110080\)	\(2.8443\)
165165.u3	165165n1	\([1, 0, 0, -8040150, 8774268867]\)	\(32445917389944971641/20917681785\)	\(37056949260716385\)	\([4]\)	\(4055040\)	\(2.4977\)	\(\Gamma_0(N)\)-optimal
165165.u4	165165n3	\([1, 0, 0, 1249020, 27489509235]\)	\(121639816754787239/184341956658895035\)	\(-326573021080588747099635\)	\([2]\)	\(16220160\)	\(3.1909\)