Elliptic curve isogeny class with Cremona label 173280bl (LMFDB label 173280.cc)

• Label: 173280bl
• Number of curves: $4$
• Conductor: $173280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 173280bl have rank \(0\).

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.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 173280.2.a.bl

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 173280bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
173280.cc3	173280bl1	\([0, 1, 0, -10950, -428400]\)	\(48228544/2025\)	\(6097146177600\)	\([2, 2]\)	\(460800\)	\(1.2180\)	\(\Gamma_0(N)\)-optimal
173280.cc2	173280bl2	\([0, 1, 0, -29000, 1326060]\)	\(111980168/32805\)	\(790190144616960\)	\([2]\)	\(921600\)	\(1.5645\)
173280.cc4	173280bl3	\([0, 1, 0, 5295, -1575297]\)	\(85184/5625\)	\(-1083937098240000\)	\([2]\)	\(921600\)	\(1.5645\)
173280.cc1	173280bl4	\([0, 1, 0, -173400, -27849960]\)	\(23937672968/45\)	\(1083937098240\)	\([2]\)	\(921600\)	\(1.5645\)