Elliptic curve isogeny class with Cremona label 44100bg (LMFDB label 44100.ca)

• Label: 44100bg
• Number of curves: $4$
• Conductor: $44100$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 44100bg 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 44100.2.a.bg

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 44100bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44100.ca3	44100bg1	\([0, 0, 0, -14700, 471625]\)	\(16384/5\)	\(107207651250000\)	\([2]\)	\(103680\)	\(1.3970\)	\(\Gamma_0(N)\)-optimal
44100.ca4	44100bg2	\([0, 0, 0, 40425, 3172750]\)	\(21296/25\)	\(-8576612100000000\)	\([2]\)	\(207360\)	\(1.7436\)
44100.ca1	44100bg3	\([0, 0, 0, -455700, -118377875]\)	\(488095744/125\)	\(2680191281250000\)	\([2]\)	\(311040\)	\(1.9463\)
44100.ca2	44100bg4	\([0, 0, 0, -400575, -148090250]\)	\(-20720464/15625\)	\(-5360382562500000000\)	\([2]\)	\(622080\)	\(2.2929\)