Elliptic curve isogeny class with Cremona label 281358cz (LMFDB label 281358.cz)

• Label: 281358cz
• Number of curves: $4$
• Conductor: $281358$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 281358cz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 281358cz do not have complex multiplication.

Modular form 281358.2.a.cz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 281358cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
281358.cz4	281358cz1	\([1, -1, 1, 16969, 1264911]\)	\(6300872423/11759616\)	\(-1008576648769536\)	\([2]\)	\(1179648\)	\(1.5636\)	\(\Gamma_0(N)\)-optimal
281358.cz3	281358cz2	\([1, -1, 1, -124151, 13401231]\)	\(2467489596697/527529024\)	\(45244118103395904\)	\([2, 2]\)	\(2359296\)	\(1.9102\)
281358.cz1	281358cz3	\([1, -1, 1, -1870511, 985075935]\)	\(8438952173768857/560166552\)	\(48043312278984792\)	\([2]\)	\(4718592\)	\(2.2568\)
281358.cz2	281358cz4	\([1, -1, 1, -635711, -183242433]\)	\(331273336732057/22285827432\)	\(1911368972118031272\)	\([2]\)	\(4718592\)	\(2.2568\)