Elliptic curve isogeny class with Cremona label 104742bg (LMFDB label 104742.bx)

• Label: 104742bg
• Number of curves: $4$
• Conductor: $104742$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 104742bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 104742bg do not have complex multiplication.

Modular form 104742.2.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 104742bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
104742.bx4	104742bg1	\([1, -1, 1, -34220, -2340817]\)	\(1108717875/45056\)	\(180087435399168\)	\([2]\)	\(405504\)	\(1.5012\)	\(\Gamma_0(N)\)-optimal
104742.bx2	104742bg2	\([1, -1, 1, -542060, -153474001]\)	\(4406910829875/7744\)	\(30952527959232\)	\([2]\)	\(811008\)	\(1.8478\)
104742.bx3	104742bg3	\([1, -1, 1, -415100, 102341935]\)	\(2714704875/21296\)	\(62052080426270352\)	\([2]\)	\(1216512\)	\(2.0505\)
104742.bx1	104742bg4	\([1, -1, 1, -700760, -56256497]\)	\(13060888875/7086244\)	\(20647829761841459628\)	\([2]\)	\(2433024\)	\(2.3971\)