Elliptic curve isogeny class with Cremona label 171600ck (LMFDB label 171600.hw)

• Label: 171600ck
• Number of curves: $2$
• Conductor: $171600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 171600ck have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 171600ck do not have complex multiplication.

Modular form 171600.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 171600ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
171600.hw2	171600ck1	\([0, 1, 0, -132808, 47734388]\)	\(-4047806261953/13066420224\)	\(-836250894336000000\)	\([2]\)	\(3096576\)	\(2.1254\)	\(\Gamma_0(N)\)-optimal
171600.hw1	171600ck2	\([0, 1, 0, -2948808, 1945718388]\)	\(44308125149913793/61165323648\)	\(3914580713472000000\)	\([2]\)	\(6193152\)	\(2.4720\)