Elliptic curve isogeny class with LMFDB label 100800.ob (Cremona label 100800fb)

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

Rank

The elliptic curves in class 100800.ob 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 100800.2.a.ob

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 100800.ob

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.ob1	100800fb1	\([0, 0, 0, -4800, -47000]\)	\(1048576/525\)	\(6123600000000\)	\([2]\)	\(147456\)	\(1.1464\)	\(\Gamma_0(N)\)-optimal
100800.ob2	100800fb2	\([0, 0, 0, 17700, -362000]\)	\(3286064/2205\)	\(-411505920000000\)	\([2]\)	\(294912\)	\(1.4930\)