Elliptic curve isogeny class with Cremona label 22743o (LMFDB label 22743.a)

• Label: 22743o
• Number of curves: $2$
• Conductor: $22743$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 22743o have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 22743o do not have complex multiplication.

Modular form 22743.2.a.o

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 22743o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22743.a2	22743o1	\([1, -1, 1, -1400387, 638139570]\)	\(8855610342769/1008273\)	\(34580181757090977\)	\([2]\)	\(483840\)	\(2.2010\)	\(\Gamma_0(N)\)-optimal
22743.a1	22743o2	\([1, -1, 1, -1514102, 528518310]\)	\(11192824869409/2963890503\)	\(101650914287951576247\)	\([2]\)	\(967680\)	\(2.5476\)