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

• Label: 16704bh
• Number of curves: $2$
• Conductor: $16704$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 16704bh have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 16704.2.a.bh

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 16704bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16704.bh2	16704bh1	\([0, 0, 0, -588, -1895056]\)	\(-117649/8118144\)	\(-1551401477996544\)	\([]\)	\(43008\)	\(1.5937\)	\(\Gamma_0(N)\)-optimal
16704.bh1	16704bh2	\([0, 0, 0, -3750348, 2803651184]\)	\(-30526075007211889/103499257854\)	\(-19779016189690773504\)	\([]\)	\(301056\)	\(2.5667\)