Elliptic curve isogeny class with LMFDB label 106722.bu (Cremona label 106722cu)

• Label: 106722.bu
• Number of curves: $4$
• Conductor: $106722$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 106722.bu have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 106722.bu do not have complex multiplication.

Modular form 106722.2.a.bu

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 106722.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106722.bu1	106722cu3	\([1, -1, 0, -4296672, 3415983808]\)	\(57736239625/255552\)	\(38828549179771509312\)	\([2]\)	\(4147200\)	\(2.6111\)
106722.bu2	106722cu4	\([1, -1, 0, -2162232, 6809316520]\)	\(-7357983625/127552392\)	\(-19380299609353454585352\)	\([2]\)	\(8294400\)	\(2.9577\)
106722.bu3	106722cu1	\([1, -1, 0, -294597, -57977375]\)	\(18609625/1188\)	\(180504619120838628\)	\([2]\)	\(1382400\)	\(2.0618\)	\(\Gamma_0(N)\)-optimal
106722.bu4	106722cu2	\([1, -1, 0, 239013, -245061041]\)	\(9938375/176418\)	\(-26804935939444536258\)	\([2]\)	\(2764800\)	\(2.4084\)