Elliptic curve isogeny class with Cremona label 51984bo (LMFDB label 51984.bq)

• Label: 51984bo
• Number of curves: $4$
• Conductor: $51984$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Rank

The elliptic curves in class 51984bo have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 51984bo has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 51984.2.a.bo

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 51984bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
51984.bq4	51984bo1	\([0, 0, 0, 0, 6859]\)	\(0\)	\(-20323820592\)	\([2]\)	\(24192\)	\(0.65680\)	\(\Gamma_0(N)\)-optimal	\(-3\)
51984.bq2	51984bo2	\([0, 0, 0, -5415, 150898]\)	\(54000\)	\(325181129472\)	\([2]\)	\(48384\)	\(1.0034\)		\(-12\)
51984.bq3	51984bo3	\([0, 0, 0, 0, -185193]\)	\(0\)	\(-14816065211568\)	\([2]\)	\(72576\)	\(1.2061\)		\(-3\)
51984.bq1	51984bo4	\([0, 0, 0, -48735, -4074246]\)	\(54000\)	\(237057043385088\)	\([2]\)	\(145152\)	\(1.5527\)		\(-12\)