Elliptic curve isogeny class with Cremona label 86700c (LMFDB label 86700.p)

• Label: 86700c
• Number of curves: $2$
• Conductor: $86700$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 86700c have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 86700.2.a.c

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 86700c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86700.p1	86700c1	\([0, -1, 0, -183033, -28438938]\)	\(112377856/6885\)	\(41546790641250000\)	\([2]\)	\(995328\)	\(1.9408\)	\(\Gamma_0(N)\)-optimal
86700.p2	86700c2	\([0, -1, 0, 142092, -118823688]\)	\(3286064/65025\)	\(-6278181696900000000\)	\([2]\)	\(1990656\)	\(2.2873\)