Elliptic curve isogeny class with LMFDB label 7200.bz (Cremona label 7200bn)

• Label: 7200.bz
• Number of curves: $4$
• Conductor: $7200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7200.bz have rank \(1\).

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7200.bz do not have complex multiplication.

Modular form 7200.2.a.bz

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 7200.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7200.bz1	7200bn2	\([0, 0, 0, -108075, -13675250]\)	\(23937672968/45\)	\(262440000000\)	\([2]\)	\(24576\)	\(1.4463\)
7200.bz2	7200bn3	\([0, 0, 0, -18075, 657250]\)	\(111980168/32805\)	\(191318760000000\)	\([2]\)	\(24576\)	\(1.4463\)
7200.bz3	7200bn1	\([0, 0, 0, -6825, -209000]\)	\(48228544/2025\)	\(1476225000000\)	\([2, 2]\)	\(12288\)	\(1.0998\)	\(\Gamma_0(N)\)-optimal
7200.bz4	7200bn4	\([0, 0, 0, 3300, -776000]\)	\(85184/5625\)	\(-262440000000000\)	\([2]\)	\(24576\)	\(1.4463\)