Elliptic curve isogeny class with LMFDB label 16704.ci (Cremona label 16704k)

• Label: 16704.ci
• Number of curves: $2$
• Conductor: $16704$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 16704.ci have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 16704.ci do not have complex multiplication.

Modular form 16704.2.a.ci

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 16704.ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16704.ci1	16704k2	\([0, 0, 0, -3564, -41040]\)	\(1940598/841\)	\(2169687638016\)	\([2]\)	\(21504\)	\(1.0633\)
16704.ci2	16704k1	\([0, 0, 0, 756, -4752]\)	\(37044/29\)	\(-37408407552\)	\([2]\)	\(10752\)	\(0.71675\)	\(\Gamma_0(N)\)-optimal