Elliptic curve isogeny class with Cremona label 9200s (LMFDB label 9200.ba)

• Label: 9200s
• Number of curves: $2$
• Conductor: $9200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9200s have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9200s do not have complex multiplication.

Modular form 9200.2.a.s

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 9200s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9200.ba2	9200s1	\([0, 1, 0, 42, -37]\)	\(32000/23\)	\(-5750000\)	\([]\)	\(1152\)	\(-0.014550\)	\(\Gamma_0(N)\)-optimal
9200.ba1	9200s2	\([0, 1, 0, -458, 4463]\)	\(-42592000/12167\)	\(-3041750000\)	\([]\)	\(3456\)	\(0.53476\)