Elliptic curve isogeny class with Cremona label 106470p (LMFDB label 106470.co)

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

Rank

The elliptic curves in class 106470p 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 106470.2.a.p

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 106470p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106470.co1	106470p1	\([1, -1, 0, -7793889, -8354851075]\)	\(551105805571803/1376829440\)	\(130807170052950343680\)	\([2]\)	\(6451200\)	\(2.7374\)	\(\Gamma_0(N)\)-optimal
106470.co2	106470p2	\([1, -1, 0, -4873569, -14693697667]\)	\(-134745327251163/903920796800\)	\(-85877972932810016649600\)	\([2]\)	\(12902400\)	\(3.0840\)