Elliptic curve isogeny class with Cremona label 54450fm (LMFDB label 54450.ez)

• Label: 54450fm
• Number of curves: $2$
• Conductor: $54450$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 54450fm have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 54450.2.a.fm

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 54450fm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54450.ez1	54450fm1	\([1, -1, 1, -16539755, 26313954747]\)	\(-1693700041/32000\)	\(-9454191267064500000000\)	\([]\)	\(4561920\)	\(3.0114\)	\(\Gamma_0(N)\)-optimal
54450.ez2	54450fm2	\([1, -1, 1, 65815870, 122999458497]\)	\(106718863559/83886080\)	\(-24783595155133562880000000\)	\([]\)	\(13685760\)	\(3.5607\)