Elliptic curve isogeny class with LMFDB label 1160.c (Cremona label 1160a)

• Label: 1160.c
• Number of curves: $2$
• Conductor: $1160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1160.c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1160.c do not have complex multiplication.

Modular form 1160.2.a.c

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 1160.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1160.c1	1160a2	\([0, -1, 0, -676, -6540]\)	\(133649126224/105125\)	\(26912000\)	\([2]\)	\(384\)	\(0.35650\)
1160.c2	1160a1	\([0, -1, 0, -51, -40]\)	\(934979584/453125\)	\(7250000\)	\([2]\)	\(192\)	\(0.0099236\)	\(\Gamma_0(N)\)-optimal