Elliptic curve isogeny class with LMFDB label 91728.x (Cremona label 91728bd)

• Label: 91728.x
• Number of curves: $1$
• Conductor: $91728$
• CM: no
• Rank: $1$

Rank

The elliptic curve 91728.x1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 91728.x do not have complex multiplication.

Modular form 91728.2.a.x

Elliptic curves in class 91728.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91728.x1	91728bd1	\([0, 0, 0, -13985139, 21436017554]\)	\(-5020930768142/389191959\)	\(-23447886303646958340096\)	\([]\)	\(8515584\)	\(3.0400\)	\(\Gamma_0(N)\)-optimal