Elliptic curve isogeny class with Cremona label 164880bf (LMFDB label 164880.bk)

• Label: 164880bf
• Number of curves: $2$
• Conductor: $164880$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 164880bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(229\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 164880bf do not have complex multiplication.

Modular form 164880.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 164880bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
164880.bk2	164880bf1	\([0, 0, 0, -1062, 8991]\)	\(11356637184/3578125\)	\(41735250000\)	\([2]\)	\(98304\)	\(0.74195\)	\(\Gamma_0(N)\)-optimal
164880.bk1	164880bf2	\([0, 0, 0, -6687, -203634]\)	\(177194479824/6555125\)	\(1223343648000\)	\([2]\)	\(196608\)	\(1.0885\)