Elliptic curve isogeny class with Cremona label 286650mk (LMFDB label 286650.mk)

• Label: 286650mk
• Number of curves: $2$
• Conductor: $286650$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 286650mk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 286650mk do not have complex multiplication.

Modular form 286650.2.a.mk

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 286650mk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
286650.mk2	286650mk1	\([1, -1, 1, 132070, -398040303]\)	\(7604375/2047032\)	\(-68580466485496875000\)	\([]\)	\(7464960\)	\(2.4854\)	\(\Gamma_0(N)\)-optimal
286650.mk1	286650mk2	\([1, -1, 1, -37077305, -86902395303]\)	\(-168256703745625/30371328\)	\(-1017512106319800000000\)	\([]\)	\(22394880\)	\(3.0347\)