Elliptic curve isogeny class with Cremona label 11760cn (LMFDB label 11760.cn)

• Label: 11760cn
• Number of curves: $2$
• Conductor: $11760$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 11760cn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11760cn do not have complex multiplication.

Modular form 11760.2.a.cn

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 11760cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11760.cn2	11760cn1	\([0, 1, 0, 75, -477]\)	\(229376/675\)	\(-135475200\)	\([]\)	\(3456\)	\(0.24376\)	\(\Gamma_0(N)\)-optimal
11760.cn1	11760cn2	\([0, 1, 0, -3285, -73725]\)	\(-19539165184/46875\)	\(-9408000000\)	\([]\)	\(10368\)	\(0.79306\)