Elliptic curve isogeny class with Cremona label 106575dc (LMFDB label 106575.cz)

• Label: 106575dc
• Number of curves: $2$
• Conductor: $106575$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 106575dc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 106575dc do not have complex multiplication.

Modular form 106575.2.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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 106575dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106575.cz1	106575dc1	\([0, 1, 1, -855458, 304256369]\)	\(-301302001664/87\)	\(-19991138671875\)	\([]\)	\(1641600\)	\(1.9190\)	\(\Gamma_0(N)\)-optimal
106575.cz2	106575dc2	\([0, 1, 1, 1410792, 1495507619]\)	\(1351431663616/4984209207\)	\(-1145287556629576171875\)	\([]\)	\(8208000\)	\(2.7237\)