Elliptic curve isogeny class with LMFDB label 1776.a (Cremona label 1776a)

• Label: 1776.a
• Number of curves: $4$
• Conductor: $1776$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1776.a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1776.a do not have complex multiplication.

Modular form 1776.2.a.a

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.

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

Isogeny graph

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

Elliptic curves in class 1776.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1776.a1	1776a3	\([0, -1, 0, -7104, 232848]\)	\(38725206845188/333\)	\(340992\)	\([4]\)	\(1024\)	\(0.64704\)
1776.a2	1776a2	\([0, -1, 0, -444, 3744]\)	\(37897488592/110889\)	\(28387584\)	\([2, 2]\)	\(512\)	\(0.30047\)
1776.a3	1776a4	\([0, -1, 0, -264, 6624]\)	\(-1994709028/16867449\)	\(-17272267776\)	\([4]\)	\(1024\)	\(0.64704\)
1776.a4	1776a1	\([0, -1, 0, -39, 18]\)	\(420616192/242757\)	\(3884112\)	\([2]\)	\(256\)	\(-0.046105\)	\(\Gamma_0(N)\)-optimal