Elliptic curve isogeny class with Cremona label 21450bs (LMFDB label 21450.bw)

• Label: 21450bs
• Number of curves: $2$
• Conductor: $21450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 21450bs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21450bs do not have complex multiplication.

Modular form 21450.2.a.bs

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 21450bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21450.bw2	21450bs1	\([1, 1, 1, -16688, 1107281]\)	\(-32894113444921/15289560000\)	\(-238899375000000\)	\([2]\)	\(92160\)	\(1.4651\)	\(\Gamma_0(N)\)-optimal
21450.bw1	21450bs2	\([1, 1, 1, -291688, 60507281]\)	\(175654575624148921/21954418200\)	\(343037784375000\)	\([2]\)	\(184320\)	\(1.8117\)