Elliptic curve isogeny class with Cremona label 23273b (LMFDB label 23273.g)

• Label: 23273b
• Number of curves: $4$
• Conductor: $23273$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 23273b have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(17\)	\(1 - T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 23273b do not have complex multiplication.

Modular form 23273.2.a.b

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 23273b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23273.g4	23273b1	\([1, -1, 0, -941, 4984]\)	\(35937/17\)	\(43617348953\)	\([2]\)	\(12960\)	\(0.73568\)	\(\Gamma_0(N)\)-optimal
23273.g2	23273b2	\([1, -1, 0, -7786, -259233]\)	\(20346417/289\)	\(741494932201\)	\([2, 2]\)	\(25920\)	\(1.0822\)
23273.g3	23273b3	\([1, -1, 0, -941, -704158]\)	\(-35937/83521\)	\(-214292035406089\)	\([2]\)	\(51840\)	\(1.4288\)
23273.g1	23273b4	\([1, -1, 0, -124151, -16806336]\)	\(82483294977/17\)	\(43617348953\)	\([2]\)	\(51840\)	\(1.4288\)