Elliptic curve isogeny class with LMFDB label 100800.bf (Cremona label 100800jg)

• Label: 100800.bf
• Number of curves: $2$
• Conductor: $100800$
• CM: no
• Rank: $0$

Rank

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

See L-function page for more information

Complex multiplication

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

Modular form 100800.2.a.bf

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.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.bf1	100800jg1	\([0, 0, 0, -43875, -3537000]\)	\(474552000/49\)	\(964467000000\)	\([2]\)	\(221184\)	\(1.3322\)	\(\Gamma_0(N)\)-optimal
100800.bf2	100800jg2	\([0, 0, 0, -40500, -4104000]\)	\(-5832000/2401\)	\(-3024568512000000\)	\([2]\)	\(442368\)	\(1.6787\)