Elliptic curve isogeny class with Cremona label 65520dr (LMFDB label 65520.cs)

• Label: 65520dr
• Number of curves: $4$
• Conductor: $65520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 65520dr have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65520dr do not have complex multiplication.

Modular form 65520.2.a.dr

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 65520dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65520.cs4	65520dr1	\([0, 0, 0, -33627, 2370314]\)	\(1408317602329/2153060\)	\(6429002711040\)	\([2]\)	\(165888\)	\(1.3573\)	\(\Gamma_0(N)\)-optimal
65520.cs3	65520dr2	\([0, 0, 0, -43707, 832106]\)	\(3092354182009/1689383150\)	\(5044471055769600\)	\([2]\)	\(331776\)	\(1.7039\)
65520.cs2	65520dr3	\([0, 0, 0, -136587, -17115334]\)	\(94376601570889/12235496000\)	\(36534995288064000\)	\([2]\)	\(497664\)	\(1.9066\)
65520.cs1	65520dr4	\([0, 0, 0, -2112267, -1181581126]\)	\(349046010201856969/7245875000\)	\(21636066816000000\)	\([2]\)	\(995328\)	\(2.2532\)