Elliptic curve isogeny class with Cremona label 4160f (LMFDB label 4160.k)

• Label: 4160f
• Number of curves: $2$
• Conductor: $4160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4160f have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4160f do not have complex multiplication.

Modular form 4160.2.a.f

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 4160f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4160.k2	4160f1	\([0, 0, 0, -107, -444]\)	\(-2116874304/105625\)	\(-6760000\)	\([2]\)	\(512\)	\(0.071611\)	\(\Gamma_0(N)\)-optimal
4160.k1	4160f2	\([0, 0, 0, -1732, -27744]\)	\(140283769536/325\)	\(1331200\)	\([2]\)	\(1024\)	\(0.41818\)