Elliptic curve isogeny class with Cremona label 100800lc (LMFDB label 100800.ep)

• Label: 100800lc
• Number of curves: $4$
• Conductor: $100800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 100800lc 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 100800.2.a.lc

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 100800lc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.ep3	100800lc1	\([0, 0, 0, -25192200, -48659389000]\)	\(151591373397612544/32558203125\)	\(379758881250000000000\)	\([2]\)	\(5898240\)	\(2.9437\)	\(\Gamma_0(N)\)-optimal
100800.ep2	100800lc2	\([0, 0, 0, -28004700, -37122514000]\)	\(13015144447800784/4341909875625\)	\(810304588628640000000000\)	\([2, 2]\)	\(11796480\)	\(3.2903\)
100800.ep4	100800lc3	\([0, 0, 0, 81345300, -256041214000]\)	\(79743193254623804/84085819746075\)	\(-62769728097166003200000000\)	\([2]\)	\(23592960\)	\(3.6368\)
100800.ep1	100800lc4	\([0, 0, 0, -182354700, 920156186000]\)	\(898353183174324196/29899176238575\)	\(22319615465391283200000000\)	\([2]\)	\(23592960\)	\(3.6368\)