Elliptic curve isogeny class with LMFDB label 106470.cz (Cremona label 106470dd)

• Label: 106470.cz
• Number of curves: $2$
• Conductor: $106470$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 106470.cz have rank \(1\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 106470.2.a.cz

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 106470.cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106470.cz1	106470dd2	\([1, -1, 0, -18459, 961065]\)	\(434314041517/4592700\)	\(7355728025100\)	\([2]\)	\(294912\)	\(1.2851\)
106470.cz2	106470dd1	\([1, -1, 0, -2079, -11907]\)	\(620650477/317520\)	\(508544159760\)	\([2]\)	\(147456\)	\(0.93852\)	\(\Gamma_0(N)\)-optimal