Elliptic curve isogeny class with Cremona label 44688cl (LMFDB label 44688.bi)

• Label: 44688cl
• Number of curves: $2$
• Conductor: $44688$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 44688cl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 44688cl do not have complex multiplication.

Modular form 44688.2.a.cl

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 44688cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44688.bi1	44688cl1	\([0, -1, 0, -277552, -44806208]\)	\(4906933498657/1032471552\)	\(497538030064631808\)	\([2]\)	\(552960\)	\(2.1104\)	\(\Gamma_0(N)\)-optimal
44688.bi2	44688cl2	\([0, -1, 0, 600528, -271702080]\)	\(49702082429663/94844496096\)	\(-45704643056428253184\)	\([2]\)	\(1105920\)	\(2.4570\)