Elliptic curve isogeny class with Cremona label 54450bt (LMFDB label 54450.cl)

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

Rank

The elliptic curves in class 54450bt 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 54450.2.a.bt

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 54450bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54450.cl1	54450bt1	\([1, -1, 0, -136692, -19732784]\)	\(-1693700041/32000\)	\(-5336644500000000\)	\([]\)	\(414720\)	\(1.8124\)	\(\Gamma_0(N)\)-optimal
54450.cl2	54450bt2	\([1, -1, 0, 543933, -92559659]\)	\(106718863559/83886080\)	\(-13989693358080000000\)	\([]\)	\(1244160\)	\(2.3617\)