Elliptic curve isogeny class with Cremona label 47040fd (LMFDB label 47040.dg)

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

Rank

The elliptic curves in class 47040fd 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 47040.2.a.fd

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 47040fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.dg1	47040fd1	\([0, -1, 0, -1045, 5125]\)	\(1048576/525\)	\(63248102400\)	\([2]\)	\(36864\)	\(0.76532\)	\(\Gamma_0(N)\)-optimal
47040.dg2	47040fd2	\([0, -1, 0, 3855, 35505]\)	\(3286064/2205\)	\(-4250272481280\)	\([2]\)	\(73728\)	\(1.1119\)