Elliptic curve isogeny class with Cremona label 54450cf (LMFDB label 54450.cv)

• Label: 54450cf
• Number of curves: $2$
• Conductor: $54450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 54450cf have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 54450cf do not have complex multiplication.

Modular form 54450.2.a.cf

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 54450cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54450.cv2	54450cf1	\([1, -1, 0, 271683, -220093659]\)	\(109902239/1100000\)	\(-22197105717187500000\)	\([]\)	\(1728000\)	\(2.3933\)	\(\Gamma_0(N)\)-optimal
54450.cv1	54450cf2	\([1, -1, 0, -161717067, -791516079909]\)	\(-23178622194826561/1610510\)	\(-32498782480534218750\)	\([]\)	\(8640000\)	\(3.1980\)