Elliptic curve isogeny class with LMFDB label 76440.cn (Cremona label 76440cy)

• Label: 76440.cn
• Number of curves: $4$
• Conductor: $76440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 76440.cn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 76440.cn do not have complex multiplication.

Modular form 76440.2.a.cn

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 76440.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76440.cn1	76440cy4	\([0, 1, 0, -377120, -89050032]\)	\(49235161015876/137109375\)	\(16517919600000000\)	\([2]\)	\(589824\)	\(1.9845\)
76440.cn2	76440cy3	\([0, 1, 0, -351640, 79841600]\)	\(39914580075556/172718325\)	\(20807821535155200\)	\([2]\)	\(589824\)	\(1.9845\)
76440.cn3	76440cy2	\([0, 1, 0, -33140, -165600]\)	\(133649126224/77000625\)	\(2319115911840000\)	\([2, 2]\)	\(294912\)	\(1.6379\)
76440.cn4	76440cy1	\([0, 1, 0, 8265, -16542]\)	\(33165879296/19278675\)	\(-36289869361200\)	\([2]\)	\(147456\)	\(1.2913\)	\(\Gamma_0(N)\)-optimal