Elliptic curve isogeny class with Cremona label 117600gz (LMFDB label 117600.hv)

• Label: 117600gz
• Number of curves: $4$
• Conductor: $117600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 117600gz have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 117600.2.a.gz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 117600gz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
117600.hv3	117600gz1	\([0, 1, 0, -7758, -91512]\)	\(438976/225\)	\(26471025000000\)	\([2, 2]\)	\(294912\)	\(1.2678\)	\(\Gamma_0(N)\)-optimal
117600.hv4	117600gz2	\([0, 1, 0, 28992, -679512]\)	\(2863288/1875\)	\(-1764735000000000\)	\([2]\)	\(589824\)	\(1.6144\)
117600.hv2	117600gz3	\([0, 1, 0, -69008, 6890988]\)	\(38614472/405\)	\(381182760000000\)	\([2]\)	\(589824\)	\(1.6144\)
117600.hv1	117600gz4	\([0, 1, 0, -99633, -12127137]\)	\(14526784/15\)	\(112943040000000\)	\([2]\)	\(589824\)	\(1.6144\)