Elliptic curve isogeny class with LMFDB label 9792.bf (Cremona label 9792q)

• Label: 9792.bf
• Number of curves: $2$
• Conductor: $9792$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9792.bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(17\)	\(1 - T\)

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.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9792.bf do not have complex multiplication.

Modular form 9792.2.a.bf

Isogeny matrix

The \(i,j\) 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.

Elliptic curves in class 9792.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9792.bf1	9792q1	\([0, 0, 0, -1740, 27632]\)	\(12194500/153\)	\(7309688832\)	\([2]\)	\(4096\)	\(0.70215\)	\(\Gamma_0(N)\)-optimal
9792.bf2	9792q2	\([0, 0, 0, -300, 71984]\)	\(-31250/23409\)	\(-2236764782592\)	\([2]\)	\(8192\)	\(1.0487\)