Elliptic curve isogeny class with Cremona label 66880y (LMFDB label 66880.dd)

• Label: 66880y
• Number of curves: $4$
• Conductor: $66880$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 66880y have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1 - T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 66880y do not have complex multiplication.

Modular form 66880.2.a.y

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 66880y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
66880.dd2	66880y1	\([0, -1, 0, -33505, 2371425]\)	\(15868125221689/2528900\)	\(662935961600\)	\([2]\)	\(165888\)	\(1.2784\)	\(\Gamma_0(N)\)-optimal
66880.dd3	66880y2	\([0, -1, 0, -30305, 2839265]\)	\(-11741970526489/6395335210\)	\(-1676498753290240\)	\([2]\)	\(331776\)	\(1.6250\)
66880.dd1	66880y3	\([0, -1, 0, -79265, -5264863]\)	\(210103680895849/75449000000\)	\(19778502656000000\)	\([2]\)	\(497664\)	\(1.8277\)
66880.dd4	66880y4	\([0, -1, 0, 240735, -37328863]\)	\(5885721311824151/5692551601000\)	\(-1492268246892544000\)	\([2]\)	\(995328\)	\(2.1743\)