Elliptic curve isogeny class with Cremona label 176400dd (LMFDB label 176400.kq)

• Label: 176400dd
• Number of curves: $2$
• Conductor: $176400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 176400dd have rank \(0\).

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
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 176400.2.a.dd

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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 176400dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.kq2	176400dd1	\([0, 0, 0, -1414875, -705293750]\)	\(-9317\)	\(-33620319432000000000\)	\([]\)	\(3225600\)	\(2.4852\)	\(\Gamma_0(N)\)-optimal
176400.kq1	176400dd2	\([0, 0, 0, -36705844875, 2706767485056250]\)	\(-162677523113838677\)	\(-33620319432000000000\)	\([]\)	\(119347200\)	\(4.2906\)