Elliptic curve isogeny class with LMFDB label 123210.cu (Cremona label 123210cc)

• Label: 123210.cu
• Number of curves: $4$
• Conductor: $123210$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 123210.cu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 123210.cu do not have complex multiplication.

Modular form 123210.2.a.cu

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 123210.cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
123210.cu1	123210cc4	\([1, -1, 1, -1573238, -759112019]\)	\(8527173507/200\)	\(10100238581669400\)	\([2]\)	\(2384640\)	\(2.1830\)
123210.cu2	123210cc3	\([1, -1, 1, -94718, -12755123]\)	\(-1860867/320\)	\(-16160381730671040\)	\([2]\)	\(1192320\)	\(1.8364\)
123210.cu3	123210cc2	\([1, -1, 1, -33113, 614531]\)	\(57960603/31250\)	\(2164831657593750\)	\([2]\)	\(794880\)	\(1.6337\)
123210.cu4	123210cc1	\([1, -1, 1, 7957, 72407]\)	\(804357/500\)	\(-34637306521500\)	\([2]\)	\(397440\)	\(1.2871\)	\(\Gamma_0(N)\)-optimal