Elliptic curve isogeny class with Cremona label 65520ek (LMFDB label 65520.dw)

• Label: 65520ek
• Number of curves: $4$
• Conductor: $65520$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 65520ek have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 65520.2.a.ek

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 65520ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65520.dw3	65520ek1	\([0, 0, 0, -33627, -1988534]\)	\(1408317602329/242911305\)	\(725329270149120\)	\([2]\)	\(245760\)	\(1.5717\)	\(\Gamma_0(N)\)-optimal
65520.dw2	65520ek2	\([0, 0, 0, -155307, 21690394]\)	\(138742439989609/12224619225\)	\(36502517411942400\)	\([2, 2]\)	\(491520\)	\(1.9183\)
65520.dw4	65520ek3	\([0, 0, 0, 172293, 101035114]\)	\(189425802193991/1586486902455\)	\(-4737224506940190720\)	\([2]\)	\(983040\)	\(2.2649\)
65520.dw1	65520ek4	\([0, 0, 0, -2429787, 1457797066]\)	\(531301262949272089/4740474375\)	\(14154980636160000\)	\([4]\)	\(983040\)	\(2.2649\)