Elliptic curve isogeny class with LMFDB label 40560.bf (Cremona label 40560k)

• Label: 40560.bf
• Number of curves: $4$
• Conductor: $40560$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 40560.bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	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 40560.bf do not have complex multiplication.

Modular form 40560.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 40560.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40560.bf1	40560k4	\([0, -1, 0, -36560, 2701152]\)	\(546718898/405\)	\(4003548456960\)	\([2]\)	\(122880\)	\(1.3519\)
40560.bf2	40560k3	\([0, -1, 0, -23040, -1322400]\)	\(136835858/1875\)	\(18534946560000\)	\([2]\)	\(122880\)	\(1.3519\)
40560.bf3	40560k2	\([0, -1, 0, -2760, 24192]\)	\(470596/225\)	\(1112096793600\)	\([2, 2]\)	\(61440\)	\(1.0053\)
40560.bf4	40560k1	\([0, -1, 0, 620, 2560]\)	\(21296/15\)	\(-18534946560\)	\([2]\)	\(30720\)	\(0.65873\)	\(\Gamma_0(N)\)-optimal