Elliptic curve isogeny class with Cremona label 44100bu (LMFDB label 44100.bd)

• Label: 44100bu
• Number of curves: $2$
• Conductor: $44100$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 44100bu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 44100bu do not have complex multiplication.

Modular form 44100.2.a.bu

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 44100bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44100.bd1	44100bu1	\([0, 0, 0, -58800, 2015125]\)	\(1048576/525\)	\(11256803381250000\)	\([2]\)	\(221184\)	\(1.7728\)	\(\Gamma_0(N)\)-optimal
44100.bd2	44100bu2	\([0, 0, 0, 216825, 15520750]\)	\(3286064/2205\)	\(-756457187220000000\)	\([2]\)	\(442368\)	\(2.1193\)