Elliptic curve isogeny class with Cremona label 100800jl (LMFDB label 100800.md)

• Label: 100800jl
• Number of curves: $2$
• Conductor: $100800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 100800jl have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 100800jl do not have complex multiplication.

Modular form 100800.2.a.jl

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 100800jl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.md2	100800jl1	\([0, 0, 0, 660, 15440]\)	\(179685/686\)	\(-121385779200\)	\([]\)	\(55296\)	\(0.80964\)	\(\Gamma_0(N)\)-optimal
100800.md1	100800jl2	\([0, 0, 0, -32940, 2304720]\)	\(-30642435/56\)	\(-7223692492800\)	\([]\)	\(165888\)	\(1.3589\)