Elliptic curve isogeny class with Cremona label 183920bn (LMFDB label 183920.cg)

• Label: 183920bn
• Number of curves: $4$
• Conductor: $183920$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 183920bn have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 183920bn do not have complex multiplication.

Modular form 183920.2.a.bn

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 183920bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
183920.cg2	183920bn1	\([0, -1, 0, -1013536, 393025536]\)	\(15868125221689/2528900\)	\(18350492110438400\)	\([2]\)	\(2488320\)	\(2.1308\)	\(\Gamma_0(N)\)-optimal
183920.cg3	183920bn2	\([0, -1, 0, -916736, 471007616]\)	\(-11741970526489/6395335210\)	\(-46406559498087669760\)	\([2]\)	\(4976640\)	\(2.4774\)
183920.cg1	183920bn3	\([0, -1, 0, -2397776, -879538240]\)	\(210103680895849/75449000000\)	\(547481624121344000000\)	\([2]\)	\(7464960\)	\(2.6801\)
183920.cg4	183920bn4	\([0, -1, 0, 7282224, -6199666240]\)	\(5885721311824151/5692551601000\)	\(-41306941058331283456000\)	\([2]\)	\(14929920\)	\(3.0267\)