Elliptic curve isogeny class with LMFDB label 116160.fa (Cremona label 116160ds)

• Label: 116160.fa
• Number of curves: $4$
• Conductor: $116160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 116160.fa have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	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 116160.fa do not have complex multiplication.

Modular form 116160.2.a.fa

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 116160.fa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
116160.fa1	116160ds4	\([0, 1, 0, -5111201, 4445966655]\)	\(127191074376964/495\)	\(57470005739520\)	\([2]\)	\(1966080\)	\(2.2763\)
116160.fa2	116160ds2	\([0, 1, 0, -319601, 69319215]\)	\(124386546256/245025\)	\(7111913210265600\)	\([2, 2]\)	\(983040\)	\(1.9298\)
116160.fa3	116160ds3	\([0, 1, 0, -213121, 116362079]\)	\(-9220796644/45106875\)	\(-5236954273013760000\)	\([2]\)	\(1966080\)	\(2.2763\)
116160.fa4	116160ds1	\([0, 1, 0, -26781, 272259]\)	\(1171019776/658845\)	\(1195196525614080\)	\([2]\)	\(491520\)	\(1.5832\)	\(\Gamma_0(N)\)-optimal