Elliptic curve isogeny class with Cremona label 16704bp (LMFDB label 16704.bb)

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

Rank

The elliptic curves in class 16704bp 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 16704.2.a.bp

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 16704bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16704.bb2	16704bp1	\([0, 0, 0, 84, -176]\)	\(37044/29\)	\(-51314688\)	\([2]\)	\(3584\)	\(0.16745\)	\(\Gamma_0(N)\)-optimal
16704.bb1	16704bp2	\([0, 0, 0, -396, -1520]\)	\(1940598/841\)	\(2976251904\)	\([2]\)	\(7168\)	\(0.51402\)