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

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

Rank

The elliptic curves in class 338800.bd 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.d
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 338800.2.a.bd

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 338800.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338800.bd1	338800bd1	\([0, 1, 0, -2108, 37288]\)	\(-2141392/49\)	\(-23716000000\)	\([]\)	\(311040\)	\(0.77842\)	\(\Gamma_0(N)\)-optimal
338800.bd2	338800bd2	\([0, 1, 0, 8892, 169288]\)	\(160630448/117649\)	\(-56942116000000\)	\([]\)	\(933120\)	\(1.3277\)