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

• Label: 11760bf
• Number of curves: $4$
• Conductor: $11760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 11760bf have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 11760.2.a.bf

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 11760bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11760.co4	11760bf1	\([0, 1, 0, 180, -372]\)	\(21296/15\)	\(-451772160\)	\([2]\)	\(4608\)	\(0.34921\)	\(\Gamma_0(N)\)-optimal
11760.co3	11760bf2	\([0, 1, 0, -800, -3900]\)	\(470596/225\)	\(27106329600\)	\([2, 2]\)	\(9216\)	\(0.69578\)
11760.co1	11760bf3	\([0, 1, 0, -10600, -423340]\)	\(546718898/405\)	\(97582786560\)	\([2]\)	\(18432\)	\(1.0424\)
11760.co2	11760bf4	\([0, 1, 0, -6680, 205428]\)	\(136835858/1875\)	\(451772160000\)	\([2]\)	\(18432\)	\(1.0424\)