Elliptic curve isogeny class with LMFDB label 9360.ba (Cremona label 9360bb)

• Label: 9360.ba
• Number of curves: $4$
• Conductor: $9360$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9360.ba have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9360.2.a.ba

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 9360.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9360.ba1	9360bb4	\([0, 0, 0, -575883, 168209082]\)	\(261984288445803/42250\)	\(3406261248000\)	\([2]\)	\(82944\)	\(1.8070\)
9360.ba2	9360bb3	\([0, 0, 0, -35883, 2645082]\)	\(-63378025803/812500\)	\(-65505024000000\)	\([2]\)	\(41472\)	\(1.4604\)
9360.ba3	9360bb2	\([0, 0, 0, -8043, 166298]\)	\(520300455507/193072360\)	\(21352258437120\)	\([2]\)	\(27648\)	\(1.2576\)
9360.ba4	9360bb1	\([0, 0, 0, 1557, 18458]\)	\(3774555693/3515200\)	\(-388752998400\)	\([2]\)	\(13824\)	\(0.91107\)	\(\Gamma_0(N)\)-optimal