Elliptic curve isogeny class with LMFDB label 164560.ca (Cremona label 164560bo)

• Label: 164560.ca
• Number of curves: $4$
• Conductor: $164560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 164560.ca have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 164560.ca do not have complex multiplication.

Modular form 164560.2.a.ca

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 164560.ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
164560.ca1	164560bo3	\([0, -1, 0, -8070256, -1733050944]\)	\(8010684753304969/4456448000000\)	\(32337385370943488000000\)	\([2]\)	\(12441600\)	\(3.0096\)
164560.ca2	164560bo1	\([0, -1, 0, -4943616, 4232314880]\)	\(1841373668746009/31443200\)	\(228161727836979200\)	\([2]\)	\(4147200\)	\(2.4603\)	\(\Gamma_0(N)\)-optimal
164560.ca3	164560bo2	\([0, -1, 0, -4788736, 4509735936]\)	\(-1673672305534489/241375690000\)	\(-1751497763848560640000\)	\([2]\)	\(8294400\)	\(2.8068\)
164560.ca4	164560bo4	\([0, -1, 0, 31579024, -13754712640]\)	\(479958568556831351/289000000000000\)	\(-2097074704384000000000000\)	\([2]\)	\(24883200\)	\(3.3561\)