Elliptic curve isogeny class with LMFDB label 185130.bq (Cremona label 185130cy)

• Label: 185130.bq
• Number of curves: $4$
• Conductor: $185130$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 185130.bq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 185130.bq do not have complex multiplication.

Modular form 185130.2.a.bq

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 185130.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
185130.bq1	185130cy3	\([1, -1, 0, -4539519, -731130867]\)	\(8010684753304969/4456448000000\)	\(5755359847514112000000\)	\([2]\)	\(12441600\)	\(2.8657\)
185130.bq2	185130cy1	\([1, -1, 0, -2780784, 1785507840]\)	\(1841373668746009/31443200\)	\(40607885642860800\)	\([2]\)	\(4147200\)	\(2.3164\)	\(\Gamma_0(N)\)-optimal
185130.bq3	185130cy2	\([1, -1, 0, -2693664, 1902544848]\)	\(-1673672305534489/241375690000\)	\(-311728972130273610000\)	\([2]\)	\(8294400\)	\(2.6630\)
185130.bq4	185130cy4	\([1, -1, 0, 17763201, -5802769395]\)	\(479958568556831351/289000000000000\)	\(-373234243041000000000000\)	\([2]\)	\(24883200\)	\(3.2123\)