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

• Label: 12480.dg
• Number of curves: $4$
• Conductor: $12480$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 12480.dg have rank \(0\).

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 12480.dg 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 LMFDB 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 LMFDB labels.

Elliptic curves in class 12480.dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12480.dg1	12480cz3	\([0, 1, 0, -6625, 204575]\)	\(490757540836/2142075\)	\(140383027200\)	\([2]\)	\(24576\)	\(0.99189\)
12480.dg2	12480cz2	\([0, 1, 0, -625, -625]\)	\(1650587344/950625\)	\(15575040000\)	\([2, 2]\)	\(12288\)	\(0.64532\)
12480.dg3	12480cz1	\([0, 1, 0, -445, -3757]\)	\(9538484224/26325\)	\(26956800\)	\([2]\)	\(6144\)	\(0.29875\)	\(\Gamma_0(N)\)-optimal
12480.dg4	12480cz4	\([0, 1, 0, 2495, -2497]\)	\(26198797244/15234375\)	\(-998400000000\)	\([2]\)	\(24576\)	\(0.99189\)