Elliptic curve isogeny class with Cremona label 16650bx (LMFDB label 16650.ch)

• Label: 16650bx
• Number of curves: $2$
• Conductor: $16650$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 16650bx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 16650bx do not have complex multiplication.

Modular form 16650.2.a.bx

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 16650bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16650.ch2	16650bx1	\([1, -1, 1, -18764105, 41746941897]\)	\(-64144540676215729729/28962038218752000\)	\(-329895716585472000000000\)	\([]\)	\(1520640\)	\(3.2195\)	\(\Gamma_0(N)\)-optimal
16650.ch1	16650bx2	\([1, -1, 1, -1656908105, 25959880701897]\)	\(-44164307457093068844199489/1823508000000000\)	\(-20770895812500000000000\)	\([]\)	\(4561920\)	\(3.7688\)