Elliptic curve isogeny class with LMFDB label 242550.bh (Cremona label 242550bh)

• Label: 242550.bh
• Number of curves: $4$
• Conductor: $242550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 242550.bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 242550.bh do not have complex multiplication.

Modular form 242550.2.a.bh

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 242550.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
242550.bh1	242550bh3	\([1, -1, 0, -17667792, 28588082116]\)	\(455129268177961/4392300\)	\(5886102082317187500\)	\([2]\)	\(14155776\)	\(2.7630\)
242550.bh2	242550bh2	\([1, -1, 0, -1130292, 424719616]\)	\(119168121961/10890000\)	\(14593641526406250000\)	\([2, 2]\)	\(7077888\)	\(2.4164\)
242550.bh3	242550bh1	\([1, -1, 0, -248292, -40094384]\)	\(1263214441/211200\)	\(283028199300000000\)	\([2]\)	\(3538944\)	\(2.0698\)	\(\Gamma_0(N)\)-optimal
242550.bh4	242550bh4	\([1, -1, 0, 1295208, 1998869116]\)	\(179310732119/1392187500\)	\(-1865664399682617187500\)	\([2]\)	\(14155776\)	\(2.7630\)