Elliptic curve isogeny class with Cremona label 9522k (LMFDB label 9522.i)

• Label: 9522k
• Number of curves: $2$
• Conductor: $9522$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9522k have rank \(0\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9522.2.a.k

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.

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

Isogeny graph

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

Elliptic curves in class 9522k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9522.i2	9522k1	\([1, -1, 1, -7241, 514725]\)	\(-389017/828\)	\(-89356239031068\)	\([2]\)	\(33792\)	\(1.3659\)	\(\Gamma_0(N)\)-optimal
9522.i1	9522k2	\([1, -1, 1, -150071, 22396281]\)	\(3463512697/3174\)	\(342532249619094\)	\([2]\)	\(67584\)	\(1.7125\)