Elliptic curve isogeny class with LMFDB label 174570.k (Cremona label 174570cy)

• Label: 174570.k
• Number of curves: $4$
• Conductor: $174570$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 174570.k have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 174570.k do not have complex multiplication.

Modular form 174570.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 174570.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
174570.k1	174570cy4	\([1, 1, 0, -847733, -300776463]\)	\(455129268177961/4392300\)	\(650218035254700\)	\([2]\)	\(3244032\)	\(2.0037\)
174570.k2	174570cy2	\([1, 1, 0, -54233, -4483563]\)	\(119168121961/10890000\)	\(1612110831210000\)	\([2, 2]\)	\(1622016\)	\(1.6572\)
174570.k3	174570cy1	\([1, 1, 0, -11913, 417093]\)	\(1263214441/211200\)	\(31265179756800\)	\([2]\)	\(811008\)	\(1.3106\)	\(\Gamma_0(N)\)-optimal
174570.k4	174570cy3	\([1, 1, 0, 62147, -20986247]\)	\(179310732119/1392187500\)	\(-206093714217187500\)	\([2]\)	\(3244032\)	\(2.0037\)