Elliptic curve isogeny class with Cremona label 42560cu (LMFDB label 42560.bx)

• Label: 42560cu
• Number of curves: $4$
• Conductor: $42560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 42560cu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 42560cu do not have complex multiplication.

Modular form 42560.2.a.cu

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 42560cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42560.bx4	42560cu1	\([0, 0, 0, -2252, -6256]\)	\(4818245769/2723840\)	\(714038312960\)	\([2]\)	\(46080\)	\(0.96451\)	\(\Gamma_0(N)\)-optimal
42560.bx2	42560cu2	\([0, 0, 0, -22732, 1312656]\)	\(4955605568649/28302400\)	\(7419304345600\)	\([2, 2]\)	\(92160\)	\(1.3111\)
42560.bx3	42560cu3	\([0, 0, 0, -9932, 2782096]\)	\(-413327139849/12516028840\)	\(-3281001864232960\)	\([2]\)	\(184320\)	\(1.6577\)
42560.bx1	42560cu4	\([0, 0, 0, -363212, 84253584]\)	\(20214562937713929/665000\)	\(174325760000\)	\([4]\)	\(184320\)	\(1.6577\)