Elliptic curve isogeny class with Cremona label 40560y (LMFDB label 40560.cq)

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

Rank

The elliptic curves in class 40560y 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 40560.2.a.y

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 40560y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40560.cq4	40560y1	\([0, 1, 0, 28505, -114100]\)	\(33165879296/19278675\)	\(-1488871711969200\)	\([2]\)	\(129024\)	\(1.6008\)	\(\Gamma_0(N)\)-optimal
40560.cq3	40560y2	\([0, 1, 0, -114300, -1028052]\)	\(133649126224/77000625\)	\(95146831297440000\)	\([2, 2]\)	\(258048\)	\(1.9474\)
40560.cq2	40560y3	\([0, 1, 0, -1212800, 511751748]\)	\(39914580075556/172718325\)	\(853686646348723200\)	\([4]\)	\(516096\)	\(2.2940\)
40560.cq1	40560y4	\([0, 1, 0, -1300680, -570015900]\)	\(49235161015876/137109375\)	\(677683983600000000\)	\([2]\)	\(516096\)	\(2.2940\)