Elliptic curve isogeny class with LMFDB label 54450.ew (Cremona label 54450ej)

• Label: 54450.ew
• Number of curves: $1$
• Conductor: $54450$
• CM: no
• Rank: $1$

Rank

The elliptic curve 54450.ew1 has 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
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 54450.2.a.ew

Elliptic curves in class 54450.ew

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54450.ew1	54450ej1	\([1, -1, 1, -42394430, 106257075697]\)	\(-464798385/4\)	\(-72517944378051562500\)	\([]\)	\(4181760\)	\(2.9787\)	\(\Gamma_0(N)\)-optimal