Elliptic curve isogeny class with Cremona label 47040s (LMFDB label 47040.j)

• Label: 47040s
• Number of curves: $2$
• Conductor: $47040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 47040s have rank \(0\).

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
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 47040.2.a.s

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 47040s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.j2	47040s1	\([0, -1, 0, 19, -195]\)	\(2048/45\)	\(-15805440\)	\([2]\)	\(12288\)	\(0.061602\)	\(\Gamma_0(N)\)-optimal
47040.j1	47040s2	\([0, -1, 0, -401, -2799]\)	\(1272112/75\)	\(421478400\)	\([2]\)	\(24576\)	\(0.40818\)