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

• Label: 106560.dc
• Number of curves: $4$
• Conductor: $106560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 106560.dc have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 106560.2.a.dc

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 106560.dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106560.dc1	106560el4	\([0, 0, 0, -79788, 8355472]\)	\(2351575819592/98316585\)	\(2348573997957120\)	\([2]\)	\(589824\)	\(1.7143\)
106560.dc2	106560el2	\([0, 0, 0, -13188, -409088]\)	\(84951891136/24950025\)	\(74500375449600\)	\([2, 2]\)	\(294912\)	\(1.3677\)
106560.dc3	106560el1	\([0, 0, 0, -12063, -509888]\)	\(4160851280704/624375\)	\(29130840000\)	\([2]\)	\(147456\)	\(1.0211\)	\(\Gamma_0(N)\)-optimal
106560.dc4	106560el3	\([0, 0, 0, 35412, -2722448]\)	\(205587930808/253011735\)	\(-6043911940177920\)	\([2]\)	\(589824\)	\(1.7143\)