Elliptic curve isogeny class with Cremona label 162288et (LMFDB label 162288.r)

• Label: 162288et
• Number of curves: $1$
• Conductor: $162288$
• CM: no
• Rank: $2$

Rank

The elliptic curve 162288et1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162288et do not have complex multiplication.

Modular form 162288.2.a.et

Elliptic curves in class 162288et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162288.r1	162288et1	\([0, 0, 0, -173019, 39329066]\)	\(-3261064466/1917027\)	\(-336723905827362816\)	\([]\)	\(1843200\)	\(2.0657\)	\(\Gamma_0(N)\)-optimal