Elliptic curve isogeny class with LMFDB label 221760.cp (Cremona label 221760lp)

• Label: 221760.cp
• Number of curves: $4$
• Conductor: $221760$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 221760.cp have rank \(1\).

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 \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 221760.2.a.cp

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 221760.cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221760.cp1	221760lp3	\([0, 0, 0, -6082560588, 182590332294512]\)	\(130231365028993807856757649/4753980000\)	\(908499725844480000\)	\([2]\)	\(94371840\)	\(3.8642\)
221760.cp2	221760lp4	\([0, 0, 0, -387256908, 2740920038768]\)	\(33608860073906150870929/2466782226562500000\)	\(471409424640000000000000000\)	\([2]\)	\(94371840\)	\(3.8642\)
221760.cp3	221760lp2	\([0, 0, 0, -380160588, 2852965254512]\)	\(31794905164720991157649/192099600000000\)	\(36710805248409600000000\)	\([2, 2]\)	\(47185920\)	\(3.5177\)
221760.cp4	221760lp1	\([0, 0, 0, -23317068, 46319601008]\)	\(-7336316844655213969/604492922880000\)	\(-115520396533306490880000\)	\([2]\)	\(23592960\)	\(3.1711\)	\(\Gamma_0(N)\)-optimal