Elliptic curve isogeny class with Cremona label 161700cq (LMFDB label 161700.ch)

• Label: 161700cq
• Number of curves: $2$
• Conductor: $161700$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 161700cq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 161700cq do not have complex multiplication.

Modular form 161700.2.a.cq

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 161700cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
161700.ch1	161700cq1	\([0, -1, 0, -49653, 3526902]\)	\(57537462272/10673289\)	\(2511403555122000\)	\([2]\)	\(884736\)	\(1.6732\)	\(\Gamma_0(N)\)-optimal
161700.ch2	161700cq2	\([0, -1, 0, 98572, 20424552]\)	\(28134667888/64304361\)	\(-242091000553248000\)	\([2]\)	\(1769472\)	\(2.0197\)