Elliptic curve isogeny class with LMFDB label 100800.hx (Cremona label 100800eh)

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

Rank

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

See L-function page for more information

Complex multiplication

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

Modular form 100800.2.a.hx

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

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.hx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.hx1	100800eh2	\([0, 0, 0, -5047500, 4618150000]\)	\(-7620530425/526848\)	\(-983224811520000000000\)	\([]\)	\(4976640\)	\(2.7791\)
100800.hx2	100800eh1	\([0, 0, 0, 352500, 6550000]\)	\(2595575/1512\)	\(-2821754880000000000\)	\([]\)	\(1658880\)	\(2.2298\)	\(\Gamma_0(N)\)-optimal