Elliptic curve isogeny class with Cremona label 44352ex (LMFDB label 44352.bt)

• Label: 44352ex
• Number of curves: $4$
• Conductor: $44352$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 44352ex have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 44352ex do not have complex multiplication.

Modular form 44352.2.a.ex

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 44352ex

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44352.bt4	44352ex1	\([0, 0, 0, 249, 2504]\)	\(36594368/79233\)	\(-3696694848\)	\([2]\)	\(20480\)	\(0.52012\)	\(\Gamma_0(N)\)-optimal
44352.bt3	44352ex2	\([0, 0, 0, -1956, 27200]\)	\(277167808/53361\)	\(159335092224\)	\([2, 2]\)	\(40960\)	\(0.86669\)
44352.bt2	44352ex3	\([0, 0, 0, -9516, -332656]\)	\(3989418056/307461\)	\(7344589012992\)	\([2]\)	\(81920\)	\(1.2133\)
44352.bt1	44352ex4	\([0, 0, 0, -29676, 1967600]\)	\(120993582536/6237\)	\(148988657664\)	\([2]\)	\(81920\)	\(1.2133\)