Elliptic curve isogeny class with LMFDB label 18032.x (Cremona label 18032s)

• Label: 18032.x
• Number of curves: $2$
• Conductor: $18032$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 18032.x have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 18032.x do not have complex multiplication.

Modular form 18032.2.a.x

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 18032.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
18032.x1	18032s2	\([0, -1, 0, -54952, -4939920]\)	\(13062552753151/92\)	\(129253376\)	\([2]\)	\(24576\)	\(1.1546\)
18032.x2	18032s1	\([0, -1, 0, -3432, -76432]\)	\(-3183010111/8464\)	\(-11891310592\)	\([2]\)	\(12288\)	\(0.80801\)	\(\Gamma_0(N)\)-optimal