Elliptic curve isogeny class with Cremona label 106470s (LMFDB label 106470.m)

• Label: 106470s
• Number of curves: $4$
• Conductor: $106470$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 106470s have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 106470s do not have complex multiplication.

Modular form 106470.2.a.s

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 106470s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106470.m4	106470s1	\([1, -1, 0, -355185, -81279639]\)	\(1408317602329/2153060\)	\(7576066442058660\)	\([2]\)	\(1161216\)	\(1.9466\)	\(\Gamma_0(N)\)-optimal
106470.m3	106470s2	\([1, -1, 0, -461655, -28449225]\)	\(3092354182009/1689383150\)	\(5944506419001027150\)	\([2]\)	\(2322432\)	\(2.2932\)
106470.m2	106470s3	\([1, -1, 0, -1442700, 587898000]\)	\(94376601570889/12235496000\)	\(43053575212740456000\)	\([2]\)	\(3483648\)	\(2.4959\)
106470.m1	106470s4	\([1, -1, 0, -22310820, 40567042296]\)	\(349046010201856969/7245875000\)	\(25496377449235875000\)	\([2]\)	\(6967296\)	\(2.8425\)