Elliptic curve isogeny class with Cremona label 9522e (LMFDB label 9522.d)

• Label: 9522e
• Number of curves: $4$
• Conductor: $9522$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9522e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9522e do not have complex multiplication.

Modular form 9522.2.a.e

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 Cremona 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 Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 9522e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9522.d4	9522e1	\([1, -1, 0, 14184, 632560]\)	\(2924207/3312\)	\(-357424956124272\)	\([2]\)	\(33792\)	\(1.4789\)	\(\Gamma_0(N)\)-optimal
9522.d3	9522e2	\([1, -1, 0, -81036, 6022012]\)	\(545338513/171396\)	\(18496741479431076\)	\([2, 2]\)	\(67584\)	\(1.8255\)
9522.d2	9522e3	\([1, -1, 0, -509526, -135293990]\)	\(135559106353/5037138\)	\(543598680145502178\)	\([2]\)	\(135168\)	\(2.1721\)
9522.d1	9522e4	\([1, -1, 0, -1176066, 491120302]\)	\(1666957239793/301806\)	\(32570349126824286\)	\([2]\)	\(135168\)	\(2.1721\)