Elliptic curve isogeny class with LMFDB label 1092.a (Cremona label 1092d)

• Label: 1092.a
• Number of curves: $2$
• Conductor: $1092$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1092.a have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 1092.a do not have complex multiplication.

Modular form 1092.2.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.

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

Isogeny graph

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

Elliptic curves in class 1092.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1092.a1	1092d2	\([0, -1, 0, -484, 4264]\)	\(49081386832/819\)	\(209664\)	\([2]\)	\(288\)	\(0.15191\)
1092.a2	1092d1	\([0, -1, 0, -29, 78]\)	\(-174456832/24843\)	\(-397488\)	\([2]\)	\(144\)	\(-0.19466\)	\(\Gamma_0(N)\)-optimal