Elliptic curve isogeny class with LMFDB label 287622.bk (Cremona label 287622bk)

• Label: 287622.bk
• Number of curves: $2$
• Conductor: $287622$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 287622.bk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(19\)	\(1 - T\)
\(29\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 287622.bk do not have complex multiplication.

Modular form 287622.2.a.bk

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 287622.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
287622.bk1	287622bk2	\([1, -1, 1, -27911, -1780279]\)	\(149721291/722\)	\(11595485819574\)	\([2]\)	\(802816\)	\(1.3555\)
287622.bk2	287622bk1	\([1, -1, 1, -2681, 6005]\)	\(132651/76\)	\(1220577454692\)	\([2]\)	\(401408\)	\(1.0089\)	\(\Gamma_0(N)\)-optimal