Elliptic curve isogeny class with Cremona label 10560r (LMFDB label 10560.bu)

• Label: 10560r
• Number of curves: $4$
• Conductor: $10560$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 10560r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10560r do not have complex multiplication.

Modular form 10560.2.a.r

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 10560r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10560.bu4	10560r1	\([0, 1, 0, -221, -285]\)	\(1171019776/658845\)	\(674657280\)	\([2]\)	\(4096\)	\(0.38425\)	\(\Gamma_0(N)\)-optimal
10560.bu2	10560r2	\([0, 1, 0, -2641, -53041]\)	\(124386546256/245025\)	\(4014489600\)	\([2, 2]\)	\(8192\)	\(0.73082\)
10560.bu1	10560r3	\([0, 1, 0, -42241, -3355681]\)	\(127191074376964/495\)	\(32440320\)	\([2]\)	\(16384\)	\(1.0774\)
10560.bu3	10560r4	\([0, 1, 0, -1761, -88065]\)	\(-9220796644/45106875\)	\(-2956124160000\)	\([2]\)	\(16384\)	\(1.0774\)