Elliptic curve isogeny class with Cremona label 86700bj (LMFDB label 86700.bi)

• Label: 86700bj
• Number of curves: $2$
• Conductor: $86700$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 86700bj have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 86700bj do not have complex multiplication.

Modular form 86700.2.a.bj

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 86700bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86700.bi2	86700bj1	\([0, 1, 0, -3853, -135937]\)	\(-40960/27\)	\(-4170971923200\)	\([]\)	\(165888\)	\(1.1225\)	\(\Gamma_0(N)\)-optimal
86700.bi1	86700bj2	\([0, 1, 0, -350653, -80038657]\)	\(-30866268160/3\)	\(-463441324800\)	\([]\)	\(497664\)	\(1.6718\)