Elliptic curve isogeny class with Cremona label 176400pj (LMFDB label 176400.kz)

• Label: 176400pj
• Number of curves: $4$
• Conductor: $176400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 176400pj 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 176400.2.a.pj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 176400pj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.kz3	176400pj1	\([0, 0, 0, -400575, 97154750]\)	\(20720464/105\)	\(36021770820000000\)	\([2]\)	\(1179648\)	\(2.0235\)	\(\Gamma_0(N)\)-optimal
176400.kz2	176400pj2	\([0, 0, 0, -621075, -21694750]\)	\(19307236/11025\)	\(15129143744400000000\)	\([2, 2]\)	\(2359296\)	\(2.3700\)
176400.kz4	176400pj3	\([0, 0, 0, 2465925, -172957750]\)	\(604223422/354375\)	\(-972587812140000000000\)	\([2]\)	\(4718592\)	\(2.7166\)
176400.kz1	176400pj4	\([0, 0, 0, -7236075, -7476799750]\)	\(15267472418/36015\)	\(98843739130080000000\)	\([2]\)	\(4718592\)	\(2.7166\)