Elliptic curve isogeny class with Cremona label 398544bg (LMFDB label 398544.bg)

• Label: 398544bg
• Number of curves: $4$
• Conductor: $398544$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 398544bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(19\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 398544bg do not have complex multiplication.

Modular form 398544.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 398544bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
398544.bg3	398544bg1	\([0, -1, 0, -74847, -7856550]\)	\(61604313088/621\)	\(467447873616\)	\([2]\)	\(1382400\)	\(1.3981\)	\(\Gamma_0(N)\)-optimal
398544.bg2	398544bg2	\([0, -1, 0, -76652, -7455840]\)	\(4135597648/385641\)	\(4644562072248576\)	\([2, 2]\)	\(2764800\)	\(1.7447\)
398544.bg1	398544bg3	\([0, -1, 0, -271592, 46191648]\)	\(45989074372/7555707\)	\(363996049810295808\)	\([2]\)	\(5529600\)	\(2.0913\)
398544.bg4	398544bg4	\([0, -1, 0, 89408, -35486768]\)	\(1640689628/12223143\)	\(-588849695768558592\)	\([2]\)	\(5529600\)	\(2.0913\)