Elliptic curve isogeny class with Cremona label 47040cu (LMFDB label 47040.dt)

• Label: 47040cu
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 47040cu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 47040cu do not have complex multiplication.

Modular form 47040.2.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 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 47040cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.dt2	47040cu1	\([0, 1, 0, -12021, -510021]\)	\(1594753024/4725\)	\(569232921600\)	\([2]\)	\(110592\)	\(1.1254\)	\(\Gamma_0(N)\)-optimal
47040.dt3	47040cu2	\([0, 1, 0, -7121, -924561]\)	\(-20720464/178605\)	\(-344272070983680\)	\([2]\)	\(221184\)	\(1.4720\)
47040.dt1	47040cu3	\([0, 1, 0, -59061, 5083035]\)	\(189123395584/16078125\)	\(1936973136000000\)	\([2]\)	\(331776\)	\(1.6747\)
47040.dt4	47040cu4	\([0, 1, 0, 63439, 23531535]\)	\(14647977776/132355125\)	\(-255122605688832000\)	\([2]\)	\(663552\)	\(2.0213\)