Elliptic curve isogeny class with Cremona label 106560ft (LMFDB label 106560.el)

• Label: 106560ft
• Number of curves: $2$
• Conductor: $106560$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 106560ft have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 106560ft do not have complex multiplication.

Modular form 106560.2.a.ft

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 106560ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106560.el1	106560ft1	\([0, 0, 0, -2172, 38896]\)	\(94875856/185\)	\(2209628160\)	\([2]\)	\(73728\)	\(0.68153\)	\(\Gamma_0(N)\)-optimal
106560.el2	106560ft2	\([0, 0, 0, -1452, 65104]\)	\(-7086244/34225\)	\(-1635124838400\)	\([2]\)	\(147456\)	\(1.0281\)