Elliptic curve isogeny class with Cremona label 10086n (LMFDB label 10086.m)

• Label: 10086n
• Number of curves: $4$
• Conductor: $10086$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 10086n have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10086n do not have complex multiplication.

Modular form 10086.2.a.n

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 10086n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10086.m3	10086n1	\([1, 1, 1, -15164, 665741]\)	\(81182737/5904\)	\(28044615438864\)	\([4]\)	\(40320\)	\(1.3268\)	\(\Gamma_0(N)\)-optimal
10086.m2	10086n2	\([1, 1, 1, -48784, -3368659]\)	\(2703045457/544644\)	\(2587115774235204\)	\([2, 2]\)	\(80640\)	\(1.6734\)
10086.m1	10086n3	\([1, 1, 1, -737994, -244316475]\)	\(9357915116017/538002\)	\(2555565581866482\)	\([2]\)	\(161280\)	\(2.0199\)
10086.m4	10086n4	\([1, 1, 1, 102506, -19950043]\)	\(25076571983/50863698\)	\(-241607867582743218\)	\([2]\)	\(161280\)	\(2.0199\)