Elliptic curve isogeny class with Cremona label 221760er (LMFDB label 221760.ck)

• Label: 221760er
• Number of curves: $4$
• Conductor: $221760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 221760er have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 221760er do not have complex multiplication.

Modular form 221760.2.a.er

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 221760er

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221760.ck3	221760er1	\([0, 0, 0, -8508, 146288]\)	\(5702413264/2525985\)	\(30170203176960\)	\([2]\)	\(524288\)	\(1.2822\)	\(\Gamma_0(N)\)-optimal
221760.ck2	221760er2	\([0, 0, 0, -66828, -6548848]\)	\(690862540036/12006225\)	\(573606332006400\)	\([2, 2]\)	\(1048576\)	\(1.6287\)
221760.ck4	221760er3	\([0, 0, 0, -2028, -18705328]\)	\(-9653618/1581886845\)	\(-151151641887375360\)	\([2]\)	\(2097152\)	\(1.9753\)
221760.ck1	221760er4	\([0, 0, 0, -1064748, -422881072]\)	\(1397097631688978/433125\)	\(41385738240000\)	\([2]\)	\(2097152\)	\(1.9753\)