Elliptic curve isogeny class with Cremona label 4400bb (LMFDB label 4400.n)

• Label: 4400bb
• Number of curves: $2$
• Conductor: $4400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 4400bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4400bb do not have complex multiplication.

Modular form 4400.2.a.bb

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 4400bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4400.n2	4400bb1	\([0, 0, 0, -500, -3125]\)	\(442368/121\)	\(3781250000\)	\([2]\)	\(1920\)	\(0.54549\)	\(\Gamma_0(N)\)-optimal
4400.n1	4400bb2	\([0, 0, 0, -7375, -243750]\)	\(88723728/11\)	\(5500000000\)	\([2]\)	\(3840\)	\(0.89206\)