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

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

Rank

The elliptic curves in class 11760bd 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 11760.2.a.bd

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 11760bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11760.ck3	11760bd1	\([0, 1, 0, -1780, -29380]\)	\(20720464/105\)	\(3162405120\)	\([2]\)	\(6144\)	\(0.66943\)	\(\Gamma_0(N)\)-optimal
11760.ck2	11760bd2	\([0, 1, 0, -2760, 5508]\)	\(19307236/11025\)	\(1328210150400\)	\([2, 2]\)	\(12288\)	\(1.0160\)
11760.ck1	11760bd3	\([0, 1, 0, -32160, 2204628]\)	\(15267472418/36015\)	\(8677639649280\)	\([2]\)	\(24576\)	\(1.3626\)
11760.ck4	11760bd4	\([0, 1, 0, 10960, 54900]\)	\(604223422/354375\)	\(-85384938240000\)	\([4]\)	\(24576\)	\(1.3626\)