Elliptic curve isogeny class with LMFDB label 10944.bd (Cremona label 10944o)

• Label: 10944.bd
• Number of curves: $4$
• Conductor: $10944$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 10944.bd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10944.bd do not have complex multiplication.

Modular form 10944.2.a.bd

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 10944.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10944.bd1	10944o3	\([0, 0, 0, -246540, 47116784]\)	\(8671983378625/82308\)	\(15729303748608\)	\([2]\)	\(55296\)	\(1.6945\)
10944.bd2	10944o4	\([0, 0, 0, -240780, 49423088]\)	\(-8078253774625/846825858\)	\(-161830941617553408\)	\([2]\)	\(110592\)	\(2.0411\)
10944.bd3	10944o1	\([0, 0, 0, -4620, -9232]\)	\(57066625/32832\)	\(6274292908032\)	\([2]\)	\(18432\)	\(1.1452\)	\(\Gamma_0(N)\)-optimal
10944.bd4	10944o2	\([0, 0, 0, 18420, -73744]\)	\(3616805375/2105352\)	\(-402339032727552\)	\([2]\)	\(36864\)	\(1.4918\)