Elliptic curve isogeny class with Cremona label 101568p (LMFDB label 101568.cv)

• Label: 101568p
• Number of curves: $2$
• Conductor: $101568$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 101568p 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.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 101568.2.a.p

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 101568p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
101568.cv2	101568p1	\([0, 1, 0, -6154033, -5930455441]\)	\(-10627137250000/110008287\)	\(-266816300046944550912\)	\([2]\)	\(3784704\)	\(2.7371\)	\(\Gamma_0(N)\)-optimal
101568.cv1	101568p2	\([0, 1, 0, -98707873, -377497101505]\)	\(10963069081334500/1156923\)	\(11224096755518472192\)	\([2]\)	\(7569408\)	\(3.0836\)