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

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

Rank

The elliptic curves in class 242550.nr 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.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 242550.2.a.nr

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 242550.nr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
242550.nr1	242550nr4	\([1, -1, 1, -56929655, -165317372153]\)	\(15226621995131793/2324168\)	\(3114607404880125000\)	\([2]\)	\(18874368\)	\(2.9542\)
242550.nr2	242550nr3	\([1, -1, 1, -6655655, 2539575847]\)	\(24331017010833/12004097336\)	\(16086638509611775875000\)	\([2]\)	\(18874368\)	\(2.9542\)
242550.nr3	242550nr2	\([1, -1, 1, -3568655, -2566322153]\)	\(3750606459153/45914176\)	\(61529387100489000000\)	\([2, 2]\)	\(9437184\)	\(2.6076\)
242550.nr4	242550nr1	\([1, -1, 1, -40655, -103778153]\)	\(-5545233/3469312\)	\(-4649209887168000000\)	\([2]\)	\(4718592\)	\(2.2610\)	\(\Gamma_0(N)\)-optimal