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

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

Rank

The elliptic curves in class 86700bi 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
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	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 86700bi do not have complex multiplication.

Modular form 86700.2.a.bi

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 86700bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86700.bm1	86700bi1	\([0, 1, 0, -45758, 6785613]\)	\(-1755904/2295\)	\(-13848930213750000\)	\([]\)	\(497664\)	\(1.7902\)	\(\Gamma_0(N)\)-optimal
86700.bm2	86700bi2	\([0, 1, 0, 387742, -130633887]\)	\(1068359936/1842375\)	\(-11117613421593750000\)	\([]\)	\(1492992\)	\(2.3395\)