Elliptic curve isogeny class with LMFDB label 189728.cn (Cremona label 189728cv)

• Label: 189728.cn
• Number of curves: $2$
• Conductor: $189728$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 189728.cn have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 189728.cn do not have complex multiplication.

Modular form 189728.2.a.cn

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 189728.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
189728.cn1	189728cv2	\([0, -1, 0, -428864, -107565016]\)	\(238328\)	\(36602304701709824\)	\([2]\)	\(2293760\)	\(2.0329\)
189728.cn2	189728cv1	\([0, -1, 0, -13834, -3309480]\)	\(-64\)	\(-4575288087713728\)	\([2]\)	\(1146880\)	\(1.6863\)	\(\Gamma_0(N)\)-optimal