Elliptic curve isogeny class with LMFDB label 189630.bd (Cremona label 189630dx)

• Label: 189630.bd
• Number of curves: $2$
• Conductor: $189630$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 189630.bd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 189630.bd do not have complex multiplication.

Modular form 189630.2.a.bd

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 189630.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
189630.bd1	189630dx2	\([1, -1, 0, -73107225, -240577441875]\)	\(503835593418244309249/898614000000\)	\(77070637056294000000\)	\([2]\)	\(23224320\)	\(3.0743\)
189630.bd2	189630dx1	\([1, -1, 0, -4522905, -3838086099]\)	\(-119305480789133569/5200091136000\)	\(-445991645581203456000\)	\([2]\)	\(11612160\)	\(2.7277\)	\(\Gamma_0(N)\)-optimal