Elliptic curve isogeny class with Cremona label 384370by (LMFDB label 384370.by)

• Label: 384370by
• Number of curves: $2$
• Conductor: $384370$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 384370by have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(17\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 384370by do not have complex multiplication.

Modular form 384370.2.a.by

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 384370by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
384370.by1	384370by1	\([1, 1, 1, -472521, 130652279]\)	\(-483385461758641/26693632000\)	\(-644319384260608000\)	\([]\)	\(10886400\)	\(2.1751\)	\(\Gamma_0(N)\)-optimal
384370.by2	384370by2	\([1, 1, 1, 2533079, 258922039]\)	\(74469146542554959/44285662466080\)	\(-1068948233485716159520\)	\([]\)	\(32659200\)	\(2.7244\)