Elliptic curve isogeny class with Cremona label 382347by (LMFDB label 382347.by)

• Label: 382347by
• Number of curves: $3$
• Conductor: $382347$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 382347by have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 382347by do not have complex multiplication.

Modular form 382347.2.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.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 382347by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
382347.by3	382347by1	\([0, 0, 1, -279113310, 1784982342393]\)	\(31363160518656000/198257271191\)	\(15201087426081845680761117\)	\([]\)	\(68677632\)	\(3.6692\)	\(\Gamma_0(N)\)-optimal
382347.by1	382347by2	\([0, 0, 1, -22573766880, 1305431738158952]\)	\(22759502184972288000/5831\)	\(325923820304425727013\)	\([]\)	\(206032896\)	\(4.2185\)
382347.by2	382347by3	\([0, 0, 1, -1736280210, -26654820906618]\)	\(838870874148864000/40675641638471\)	\(28068710057873390746207030293\)	\([]\)	\(206032896\)	\(4.2185\)