Elliptic curve isogeny class with Cremona label 130050ck (LMFDB label 130050.ha)

• Label: 130050ck
• Number of curves: $2$
• Conductor: $130050$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 130050ck have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 130050ck do not have complex multiplication.

Modular form 130050.2.a.ck

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 130050ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130050.ha2	130050ck1	\([1, -1, 1, -104301455, 412280185047]\)	\(-1579268174113/10077696\)	\(-800755958203735896000000\)	\([]\)	\(33312384\)	\(3.4239\)	\(\Gamma_0(N)\)-optimal
130050.ha1	130050ck2	\([1, -1, 1, -8461314455, 299576631559047]\)	\(-843137281012581793/216\)	\(-17162979213900375000\)	\([]\)	\(99937152\)	\(3.9732\)