Elliptic curve isogeny class with Cremona label 9360bs (LMFDB label 9360.bn)

• Label: 9360bs
• Number of curves: $4$
• Conductor: $9360$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9360bs have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9360bs do not have complex multiplication.

Modular form 9360.2.a.bs

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 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.

Elliptic curves in class 9360bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9360.bn3	9360bs1	\([0, 0, 0, -1947, 32074]\)	\(273359449/9360\)	\(27948810240\)	\([2]\)	\(6144\)	\(0.77634\)	\(\Gamma_0(N)\)-optimal
9360.bn2	9360bs2	\([0, 0, 0, -4827, -84854]\)	\(4165509529/1368900\)	\(4087513497600\)	\([2, 2]\)	\(12288\)	\(1.1229\)
9360.bn1	9360bs3	\([0, 0, 0, -69627, -7070294]\)	\(12501706118329/2570490\)	\(7675442012160\)	\([2]\)	\(24576\)	\(1.4695\)
9360.bn4	9360bs4	\([0, 0, 0, 13893, -582806]\)	\(99317171591/106616250\)	\(-318354416640000\)	\([2]\)	\(24576\)	\(1.4695\)