Elliptic curve isogeny class with Cremona label 338800bf (LMFDB label 338800.bf)

• Label: 338800bf
• Number of curves: $2$
• Conductor: $338800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 338800bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 338800bf do not have complex multiplication.

Modular form 338800.2.a.bf

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 338800bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338800.bf2	338800bf1	\([0, 1, 0, -1613333, 56152963]\)	\(6553600/3773\)	\(267363986120000000000\)	\([]\)	\(9331200\)	\(2.6092\)	\(\Gamma_0(N)\)-optimal
338800.bf1	338800bf2	\([0, 1, 0, -86313333, -308675347037]\)	\(1003555225600/9317\)	\(660225353480000000000\)	\([]\)	\(27993600\)	\(3.1585\)