Elliptic curve isogeny class with LMFDB label 16830.bs (Cremona label 16830by)

• Label: 16830.bs
• Number of curves: $2$
• Conductor: $16830$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 16830.bs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.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 16830.bs do not have complex multiplication.

Modular form 16830.2.a.bs

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 16830.bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16830.bs1	16830by2	\([1, -1, 1, -6188, -183769]\)	\(35940267099001/448014600\)	\(326602643400\)	\([2]\)	\(36864\)	\(1.0190\)
16830.bs2	16830by1	\([1, -1, 1, -68, -7513]\)	\(-47045881/33570240\)	\(-24472704960\)	\([2]\)	\(18432\)	\(0.67246\)	\(\Gamma_0(N)\)-optimal