Elliptic curve isogeny class with Cremona label 61050bk (LMFDB label 61050.bt)

• Label: 61050bk
• Number of curves: $2$
• Conductor: $61050$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 61050bk have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 61050bk do not have complex multiplication.

Modular form 61050.2.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 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 61050bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61050.bt1	61050bk1	\([1, 1, 1, -923638, 328676531]\)	\(5577108481460841625/233729407061568\)	\(3652021985337000000\)	\([2]\)	\(1824768\)	\(2.3266\)	\(\Gamma_0(N)\)-optimal
61050.bt2	61050bk2	\([1, 1, 1, 445362, 1221264531]\)	\(625234740274982375/41585929145369928\)	\(-649780142896405125000\)	\([2]\)	\(3649536\)	\(2.6732\)