Elliptic curve isogeny class with Cremona label 176400cq (LMFDB label 176400.tf)

• Label: 176400cq
• Number of curves: $2$
• Conductor: $176400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 176400cq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 176400cq do not have complex multiplication.

Modular form 176400.2.a.cq

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 176400cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.tf2	176400cq1	\([0, 0, 0, -147000, 31727500]\)	\(-40960/27\)	\(-231568526700000000\)	\([]\)	\(2177280\)	\(2.0329\)	\(\Gamma_0(N)\)-optimal
176400.tf1	176400cq2	\([0, 0, 0, -13377000, 18831557500]\)	\(-30866268160/3\)	\(-25729836300000000\)	\([]\)	\(6531840\)	\(2.5822\)