Elliptic curve isogeny class with Cremona label 116160do (LMFDB label 116160.gz)

• Label: 116160do
• Number of curves: $2$
• Conductor: $116160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 116160do 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 116160do do not have complex multiplication.

Modular form 116160.2.a.do

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 116160do

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
116160.gz1	116160do1	\([0, 1, 0, -1976, -26490]\)	\(7529536/1815\)	\(205784525760\)	\([2]\)	\(122880\)	\(0.88189\)	\(\Gamma_0(N)\)-optimal
116160.gz2	116160do2	\([0, 1, 0, 4679, -160921]\)	\(1560896/2475\)	\(-17959376793600\)	\([2]\)	\(245760\)	\(1.2285\)