Elliptic curve isogeny class with Cremona label 8670q (LMFDB label 8670.s)

• Label: 8670q
• Number of curves: $2$
• Conductor: $8670$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8670q have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8670q do not have complex multiplication.

Modular form 8670.2.a.q

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 8670q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8670.s2	8670q1	\([1, 1, 1, 71955, 16951587]\)	\(347428927/1244160\)	\(-147542292422507520\)	\([2]\)	\(108800\)	\(1.9773\)	\(\Gamma_0(N)\)-optimal
8670.s1	8670q2	\([1, 1, 1, -714125, 202152035]\)	\(339630096833/47239200\)	\(5601996415417082400\)	\([2]\)	\(217600\)	\(2.3239\)