Elliptic curve isogeny class with LMFDB label 43200.jh (Cremona label 43200eb)

• Label: 43200.jh
• Number of curves: $2$
• Conductor: $43200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 43200.jh have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 43200.jh do not have complex multiplication.

Modular form 43200.2.a.jh

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 43200.jh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43200.jh1	43200eb2	\([0, 0, 0, -51300, -4563000]\)	\(-5267712/125\)	\(-354294000000000\)	\([]\)	\(248832\)	\(1.5781\)
43200.jh2	43200eb1	\([0, 0, 0, 2700, -27000]\)	\(6912/5\)	\(-1574640000000\)	\([]\)	\(82944\)	\(1.0288\)	\(\Gamma_0(N)\)-optimal