Elliptic curve isogeny class with LMFDB label 11592.r (Cremona label 11592n)

• Label: 11592.r
• Number of curves: $1$
• Conductor: $11592$
• CM: no
• Rank: $1$

Rank

The elliptic curve 11592.r1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11592.r do not have complex multiplication.

Modular form 11592.2.a.r

Elliptic curves in class 11592.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11592.r1	11592n1	\([0, 0, 0, -3531, 114662]\)	\(-3261064466/1917027\)	\(-2862105974784\)	\([]\)	\(19200\)	\(1.0928\)	\(\Gamma_0(N)\)-optimal