Elliptic curve isogeny class with LMFDB label 101568.bf (Cremona label 101568ck)

• Label: 101568.bf
• Number of curves: $4$
• Conductor: $101568$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 101568.bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 101568.bf do not have complex multiplication.

Modular form 101568.2.a.bf

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 101568.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
101568.bf1	101568ck4	\([0, -1, 0, -1591937, 654751137]\)	\(45989074372/7555707\)	\(73303051650237923328\)	\([2]\)	\(3244032\)	\(2.5334\)
101568.bf2	101568ck2	\([0, -1, 0, -449297, -106018575]\)	\(4135597648/385641\)	\(935341396293206016\)	\([2, 2]\)	\(1622016\)	\(2.1868\)
101568.bf3	101568ck1	\([0, -1, 0, -438717, -111700035]\)	\(61604313088/621\)	\(94136613958656\)	\([2]\)	\(811008\)	\(1.8402\)	\(\Gamma_0(N)\)-optimal
101568.bf4	101568ck3	\([0, -1, 0, 524063, -503344127]\)	\(1640689628/12223143\)	\(-118585022243086467072\)	\([2]\)	\(3244032\)	\(2.5334\)