Elliptic curve isogeny class with Cremona label 129360ic (LMFDB label 129360.ie)

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

Rank

The elliptic curves in class 129360ic 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 \(\mathbb{F}_p\)
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 129360.2.a.ic

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 129360ic

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129360.ie3	129360ic1	\([0, 1, 0, -251680, -37232140]\)	\(3658671062929/880165440\)	\(424143191451893760\)	\([2]\)	\(1990656\)	\(2.0935\)	\(\Gamma_0(N)\)-optimal
129360.ie4	129360ic2	\([0, 1, 0, 595040, -233332492]\)	\(48351870250991/76871856600\)	\(-37043802346018406400\)	\([2]\)	\(3981312\)	\(2.4401\)
129360.ie1	129360ic3	\([0, 1, 0, -19020640, -31935376012]\)	\(1579250141304807889/41926500\)	\(20203973830656000\)	\([2]\)	\(5971968\)	\(2.6428\)
129360.ie2	129360ic4	\([0, 1, 0, -18997120, -32018269900]\)	\(-1573398910560073969/8138108343750\)	\(-3921675503754624000000\)	\([2]\)	\(11943936\)	\(2.9894\)