Elliptic curve isogeny class with Cremona label 40560bu (LMFDB label 40560.be)

• Label: 40560bu
• Number of curves: $4$
• Conductor: $40560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 40560bu have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40560bu do not have complex multiplication.

Modular form 40560.2.a.bu

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 40560bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40560.be4	40560bu1	\([0, -1, 0, -780160, -437915648]\)	\(-2656166199049/2658140160\)	\(-52553051535562506240\)	\([2]\)	\(1290240\)	\(2.4797\)	\(\Gamma_0(N)\)-optimal
40560.be3	40560bu2	\([0, -1, 0, -14624640, -21514752000]\)	\(17496824387403529/6580454400\)	\(130099595354151321600\)	\([2, 2]\)	\(2580480\)	\(2.8263\)
40560.be2	40560bu3	\([0, -1, 0, -16787840, -14729226240]\)	\(26465989780414729/10571870144160\)	\(209012318038682769162240\)	\([2]\)	\(5160960\)	\(3.1729\)
40560.be1	40560bu4	\([0, -1, 0, -233973120, -1377439315968]\)	\(71647584155243142409/10140000\)	\(200473981992960000\)	\([2]\)	\(5160960\)	\(3.1729\)