Elliptic curve isogeny class with LMFDB label 117600.hz (Cremona label 117600dd)

• Label: 117600.hz
• Number of curves: $4$
• Conductor: $117600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 117600.hz have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 117600.hz do not have complex multiplication.

Modular form 117600.2.a.hz

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 117600.hz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
117600.hz1	117600dd4	\([0, 1, 0, -1372408, -619289812]\)	\(303735479048/105\)	\(98825160000000\)	\([2]\)	\(1769472\)	\(2.0413\)
117600.hz2	117600dd3	\([0, 1, 0, -178033, 14372063]\)	\(82881856/36015\)	\(271176239040000000\)	\([2]\)	\(1769472\)	\(2.0413\)
117600.hz3	117600dd1	\([0, 1, 0, -86158, -9607312]\)	\(601211584/11025\)	\(1297080225000000\)	\([2, 2]\)	\(884736\)	\(1.6947\)	\(\Gamma_0(N)\)-optimal
117600.hz4	117600dd2	\([0, 1, 0, -408, -27786312]\)	\(-8/354375\)	\(-333534915000000000\)	\([2]\)	\(1769472\)	\(2.0413\)