Elliptic curve isogeny class with Cremona label 128576dc (LMFDB label 128576.dd)

• Label: 128576dc
• Number of curves: $2$
• Conductor: $128576$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 128576dc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 128576dc do not have complex multiplication.

Modular form 128576.2.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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 128576dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
128576.dd2	128576dc1	\([0, 0, 0, -60690028, 167515728464]\)	\(801581275315909089/70810888830976\)	\(2183877167697230672429056\)	\([]\)	\(32514048\)	\(3.4105\)	\(\Gamma_0(N)\)-optimal
128576.dd1	128576dc2	\([0, 0, 0, -30141076588, -2014124231133616]\)	\(98191033604529537629349729/10906239337336\)	\(336359103344998629769216\)	\([]\)	\(227598336\)	\(4.3834\)