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

• Label: 1776.j
• Number of curves: $2$
• Conductor: $1776$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1776.j have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 1776.2.a.j

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.

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

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.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1776.j1	1776c2	\([0, 1, 0, -188, 924]\)	\(2885794000/26973\)	\(6905088\)	\([2]\)	\(384\)	\(0.13349\)
1776.j2	1776c1	\([0, 1, 0, -3, 36]\)	\(-256000/36963\)	\(-591408\)	\([2]\)	\(192\)	\(-0.21308\)	\(\Gamma_0(N)\)-optimal