Elliptic curve isogeny class with Cremona label 176400kw (LMFDB label 176400.dz)

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

Rank

The elliptic curves in class 176400kw 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 176400.2.a.kw

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 176400kw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.dz1	176400kw1	\([0, 0, 0, -1826475, -950195750]\)	\(-67645179/8\)	\(-79692609024000000\)	\([]\)	\(2612736\)	\(2.2686\)	\(\Gamma_0(N)\)-optimal
176400.dz2	176400kw2	\([0, 0, 0, 231525, -2933421750]\)	\(189/512\)	\(-3718138366623744000000\)	\([]\)	\(7838208\)	\(2.8179\)