Elliptic curve isogeny class with LMFDB label 173280.bh (Cremona label 173280cg)

• Label: 173280.bh
• Number of curves: $4$
• Conductor: $173280$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 173280.bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(19\)	\(1\)

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
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 173280.bh do not have complex multiplication.

Modular form 173280.2.a.bh

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 173280.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
173280.bh1	173280cg2	\([0, -1, 0, -173400, 27849960]\)	\(23937672968/45\)	\(1083937098240\)	\([2]\)	\(921600\)	\(1.5645\)
173280.bh2	173280cg4	\([0, -1, 0, -29000, -1326060]\)	\(111980168/32805\)	\(790190144616960\)	\([2]\)	\(921600\)	\(1.5645\)
173280.bh3	173280cg1	\([0, -1, 0, -10950, 428400]\)	\(48228544/2025\)	\(6097146177600\)	\([2, 2]\)	\(460800\)	\(1.2180\)	\(\Gamma_0(N)\)-optimal
173280.bh4	173280cg3	\([0, -1, 0, 5295, 1575297]\)	\(85184/5625\)	\(-1083937098240000\)	\([2]\)	\(921600\)	\(1.5645\)