Elliptic curve isogeny class with Cremona label 4400r (LMFDB label 4400.t)

• Label: 4400r
• Number of curves: $2$
• Conductor: $4400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4400r have rank \(1\).

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

See L-function page for more information

Complex multiplication

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

Modular form 4400.2.a.r

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 4400r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4400.t1	4400r1	\([0, 1, 0, -408, -8812]\)	\(-117649/440\)	\(-28160000000\)	\([]\)	\(2304\)	\(0.69076\)	\(\Gamma_0(N)\)-optimal
4400.t2	4400r2	\([0, 1, 0, 3592, 207188]\)	\(80062991/332750\)	\(-21296000000000\)	\([]\)	\(6912\)	\(1.2401\)