Elliptic curve isogeny class with Cremona label 86700bc (LMFDB label 86700.bt)

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

Rank

The elliptic curves in class 86700bc 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 86700.2.a.bc

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 86700bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86700.bt1	86700bc1	\([0, 1, 0, -3182766633, 69105455260488]\)	\(590887175978458660864/57171426328125\)	\(344994811955883457031250000\)	\([2]\)	\(46448640\)	\(4.1281\)	\(\Gamma_0(N)\)-optimal
86700.bt2	86700bc2	\([0, 1, 0, -2945750508, 79832805077988]\)	\(-29279123829148431184/11573052978515625\)	\(-1117381459238305664062500000000\)	\([2]\)	\(92897280\)	\(4.4747\)