Elliptic curve isogeny class with Cremona label 129360ex (LMFDB label 129360.cq)

• Label: 129360ex
• Number of curves: $4$
• Conductor: $129360$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 129360ex have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129360ex do not have complex multiplication.

Modular form 129360.2.a.ex

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 129360ex

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129360.cq3	129360ex1	\([0, -1, 0, -1092520, -439168400]\)	\(299270638153369/1069200\)	\(515237113036800\)	\([2]\)	\(1474560\)	\(2.0409\)	\(\Gamma_0(N)\)-optimal
129360.cq2	129360ex2	\([0, -1, 0, -1108200, -425896848]\)	\(312341975961049/17862322500\)	\(8607680019671040000\)	\([2, 2]\)	\(2949120\)	\(2.3875\)
129360.cq4	129360ex3	\([0, -1, 0, 796920, -1739667600]\)	\(116149984977671/2779502343750\)	\(-1339415229398400000000\)	\([2]\)	\(5898240\)	\(2.7341\)
129360.cq1	129360ex4	\([0, -1, 0, -3264200, 1737002352]\)	\(7981893677157049/1917731420550\)	\(924136177239191347200\)	\([2]\)	\(5898240\)	\(2.7341\)