Elliptic curve isogeny class with Cremona label 54450fa (LMFDB label 54450.gm)

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

Rank

The elliptic curves in class 54450fa 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.b
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 54450.2.a.fa

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 54450fa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54450.gm1	54450fa1	\([1, -1, 1, -2607980, -1581166353]\)	\(129392980254539/3583180800\)	\(54324324172800000000\)	\([2]\)	\(2064384\)	\(2.5663\)	\(\Gamma_0(N)\)-optimal
54450.gm2	54450fa2	\([1, -1, 1, 560020, -5180014353]\)	\(1281177907381/765275040000\)	\(-11602275094327500000000\)	\([2]\)	\(4128768\)	\(2.9128\)