Elliptic curve isogeny class with Cremona label 165825bd (LMFDB label 165825.bg)

• Label: 165825bd
• Number of curves: $2$
• Conductor: $165825$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 165825bd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(67\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 165825bd do not have complex multiplication.

Modular form 165825.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 165825bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
165825.bg2	165825bd1	\([1, -1, 0, -23742, 1234791]\)	\(129938649625/17924577\)	\(204172134890625\)	\([2]\)	\(414720\)	\(1.4725\)	\(\Gamma_0(N)\)-optimal
165825.bg1	165825bd2	\([1, -1, 0, -99117, -10749834]\)	\(9454162623625/1068251283\)	\(12168049770421875\)	\([2]\)	\(829440\)	\(1.8191\)