Elliptic curve isogeny class with Cremona label 12480dg (LMFDB label 12480.co)

• Label: 12480dg
• Number of curves: $4$
• Conductor: $12480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 12480dg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12480dg do not have complex multiplication.

Modular form 12480.2.a.dg

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 12480dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12480.co4	12480dg1	\([0, 1, 0, -18465, -1601697]\)	\(-2656166199049/2658140160\)	\(-696815494103040\)	\([2]\)	\(61440\)	\(1.5438\)	\(\Gamma_0(N)\)-optimal
12480.co3	12480dg2	\([0, 1, 0, -346145, -78475425]\)	\(17496824387403529/6580454400\)	\(1725026638233600\)	\([2, 2]\)	\(122880\)	\(1.8904\)
12480.co1	12480dg3	\([0, 1, 0, -5537825, -5017839777]\)	\(71647584155243142409/10140000\)	\(2658140160000\)	\([2]\)	\(245760\)	\(2.2370\)
12480.co2	12480dg4	\([0, 1, 0, -397345, -53786785]\)	\(26465989780414729/10571870144160\)	\(2771352327070679040\)	\([4]\)	\(245760\)	\(2.2370\)