Elliptic curve isogeny class with LMFDB label 129600.cy (Cremona label 129600bh)

• Label: 129600.cy
• Number of curves: $4$
• Conductor: $129600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 129600.cy have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129600.cy do not have complex multiplication.

Modular form 129600.2.a.cy

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 129600.cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129600.cy1	129600bh4	\([0, 0, 0, -15511500, -23514138000]\)	\(-189613868625/128\)	\(-278628139008000000\)	\([]\)	\(3483648\)	\(2.6631\)
129600.cy2	129600bh3	\([0, 0, 0, -151500, -46106000]\)	\(-1159088625/2097152\)	\(-695784701952000000\)	\([]\)	\(1161216\)	\(2.1138\)
129600.cy3	129600bh1	\([0, 0, 0, -7500, 262000]\)	\(-140625/8\)	\(-2654208000000\)	\([]\)	\(165888\)	\(1.1409\)	\(\Gamma_0(N)\)-optimal
129600.cy4	129600bh2	\([0, 0, 0, 40500, 486000]\)	\(3375/2\)	\(-4353564672000000\)	\([]\)	\(497664\)	\(1.6902\)