Elliptic curve isogeny class with Cremona label 12480bf (LMFDB label 12480.cu)

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

Rank

The elliptic curves in class 12480bf 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 12480.2.a.bf

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 12480bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12480.cu4	12480bf1	\([0, 1, 0, 675, 675]\)	\(33165879296/19278675\)	\(-19741363200\)	\([2]\)	\(6144\)	\(0.66494\)	\(\Gamma_0(N)\)-optimal
12480.cu3	12480bf2	\([0, 1, 0, -2705, 2703]\)	\(133649126224/77000625\)	\(1261578240000\)	\([2, 2]\)	\(12288\)	\(1.0115\)
12480.cu2	12480bf3	\([0, 1, 0, -28705, -1874497]\)	\(39914580075556/172718325\)	\(11319268147200\)	\([2]\)	\(24576\)	\(1.3581\)
12480.cu1	12480bf4	\([0, 1, 0, -30785, 2063775]\)	\(49235161015876/137109375\)	\(8985600000000\)	\([2]\)	\(24576\)	\(1.3581\)