Elliptic curve isogeny class with LMFDB label 66066.cl (Cremona label 66066ck)

• Label: 66066.cl
• Number of curves: $4$
• Conductor: $66066$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 66066.cl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	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 66066.cl do not have complex multiplication.

Modular form 66066.2.a.cl

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 66066.cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
66066.cl1	66066ck4	\([1, 0, 0, -9333398, -1554270684]\)	\(50755950018496437625/28784156647454208\)	\(50992889334520624178688\)	\([2]\)	\(7464960\)	\(3.0471\)
66066.cl2	66066ck2	\([1, 0, 0, -6877703, -6943011855]\)	\(20309435779581663625/64280368152\)	\(113876593283725272\)	\([2]\)	\(2488320\)	\(2.4978\)
66066.cl3	66066ck3	\([1, 0, 0, -5926038, 5525541924]\)	\(12991547986467765625/71708514189312\)	\(127036007105731756032\)	\([2]\)	\(3732480\)	\(2.7005\)
66066.cl4	66066ck1	\([1, 0, 0, -435663, -105430599]\)	\(5162020164015625/278574424128\)	\(493511585382623808\)	\([2]\)	\(1244160\)	\(2.1512\)	\(\Gamma_0(N)\)-optimal