Elliptic curve isogeny class with Cremona label 161700da (LMFDB label 161700.bf)

• Label: 161700da
• Number of curves: $2$
• Conductor: $161700$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 161700da have rank \(0\).

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 \(\mathbb{F}_p\)
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 161700.2.a.da

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 161700da

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
161700.bf1	161700da1	\([0, -1, 0, -6747708, -6744386088]\)	\(-2888047810000/35937\)	\(-422795211300000000\)	\([]\)	\(4898880\)	\(2.5293\)	\(\Gamma_0(N)\)-optimal
161700.bf2	161700da2	\([0, -1, 0, -3072708, -14032646088]\)	\(-272709010000/7073843073\)	\(-83223056369537700000000\)	\([]\)	\(14696640\)	\(3.0786\)