Elliptic curve isogeny class with Cremona label 42450bf (LMFDB label 42450.bd)

• Label: 42450bf
• Number of curves: $2$
• Conductor: $42450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 42450bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(283\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 42450bf do not have complex multiplication.

Modular form 42450.2.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 42450bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42450.bd2	42450bf1	\([1, 0, 0, -7263, -322983]\)	\(-21694295069/10432512\)	\(-20376000000000\)	\([2]\)	\(107520\)	\(1.2594\)	\(\Gamma_0(N)\)-optimal
42450.bd1	42450bf2	\([1, 0, 0, -127263, -17482983]\)	\(116707927418909/15377088\)	\(30033375000000\)	\([2]\)	\(215040\)	\(1.6060\)