Elliptic curve isogeny class with Cremona label 100800oe (LMFDB label 100800.qa)

• Label: 100800oe
• Number of curves: $4$
• Conductor: $100800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 100800oe have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 100800.2.a.oe

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 100800oe

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.qa4	100800oe1	\([0, 0, 0, 6000, -61000]\)	\(2048000/1323\)	\(-15431472000000\)	\([2]\)	\(221184\)	\(1.2195\)	\(\Gamma_0(N)\)-optimal
100800.qa3	100800oe2	\([0, 0, 0, -25500, -502000]\)	\(9826000/5103\)	\(952342272000000\)	\([2]\)	\(442368\)	\(1.5661\)
100800.qa2	100800oe3	\([0, 0, 0, -102000, -12913000]\)	\(-10061824000/352947\)	\(-4116773808000000\)	\([2]\)	\(663552\)	\(1.7688\)
100800.qa1	100800oe4	\([0, 0, 0, -1645500, -812446000]\)	\(2640279346000/3087\)	\(576108288000000\)	\([2]\)	\(1327104\)	\(2.1154\)