Elliptic curve isogeny class with LMFDB label 84700.bd (Cremona label 84700o)

• Label: 84700.bd
• Number of curves: $2$
• Conductor: $84700$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 84700.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.ac
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 84700.bd do not have complex multiplication.

Modular form 84700.2.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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 84700.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84700.bd1	84700o2	\([0, -1, 0, -255108, -37195288]\)	\(194672/49\)	\(462157747436000000\)	\([2]\)	\(1216512\)	\(2.0995\)
84700.bd2	84700o1	\([0, -1, 0, -88733, 9722462]\)	\(131072/7\)	\(4126408459250000\)	\([2]\)	\(608256\)	\(1.7529\)	\(\Gamma_0(N)\)-optimal