Elliptic curve isogeny class with Cremona label 10944b (LMFDB label 10944.bi)

• Label: 10944b
• Number of curves: $2$
• Conductor: $10944$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 10944b have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 10944.2.a.b

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 10944b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10944.bi1	10944b1	\([0, 0, 0, -540, 3024]\)	\(54000/19\)	\(6127239168\)	\([2]\)	\(3072\)	\(0.57929\)	\(\Gamma_0(N)\)-optimal
10944.bi2	10944b2	\([0, 0, 0, 1620, 21168]\)	\(364500/361\)	\(-465670176768\)	\([2]\)	\(6144\)	\(0.92586\)