Elliptic curve isogeny class with LMFDB label 163370.k (Cremona label 163370t)

• Label: 163370.k
• Number of curves: $2$
• Conductor: $163370$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 163370.k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1 - T\)
\(17\)	\(1 + T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 163370.k do not have complex multiplication.

Modular form 163370.2.a.k

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 163370.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163370.k1	163370t1	\([1, 1, 0, -7227, -207859]\)	\(47045881/6800\)	\(6035025030800\)	\([2]\)	\(489600\)	\(1.1777\)	\(\Gamma_0(N)\)-optimal
163370.k2	163370t2	\([1, 1, 0, 11993, -1103511]\)	\(214921799/722500\)	\(-641221409522500\)	\([2]\)	\(979200\)	\(1.5243\)