Elliptic curve isogeny class with Cremona label 116160dz (LMFDB label 116160.in)

• Label: 116160dz
• Number of curves: $4$
• Conductor: $116160$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 116160dz have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 116160.2.a.dz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 116160dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
116160.in3	116160dz1	\([0, 1, 0, -10791425, 13641134175]\)	\(299270638153369/1069200\)	\(496540849589452800\)	\([2]\)	\(3686400\)	\(2.6135\)	\(\Gamma_0(N)\)-optimal
116160.in2	116160dz2	\([0, 1, 0, -10946305, 13229246303]\)	\(312341975961049/17862322500\)	\(8295335568453795840000\)	\([2, 2]\)	\(7372800\)	\(2.9601\)
116160.in4	116160dz3	\([0, 1, 0, 7871615, 54000151775]\)	\(116149984977671/2779502343750\)	\(-1290812247663206400000000\)	\([2]\)	\(14745600\)	\(3.3067\)
116160.in1	116160dz4	\([0, 1, 0, -32242305, -53900004897]\)	\(7981893677157049/1917731420550\)	\(890602309057505801011200\)	\([2]\)	\(14745600\)	\(3.3067\)