Elliptic curve isogeny class with LMFDB label 84966.dt (Cremona label 84966ec)

• Label: 84966.dt
• Number of curves: $1$
• Conductor: $84966$
• CM: no
• Rank: $1$

Rank

The elliptic curve 84966.dt1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 84966.dt do not have complex multiplication.

Modular form 84966.2.a.dt

Elliptic curves in class 84966.dt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84966.dt1	84966ec1	\([1, 0, 0, -85261, -425511703]\)	\(-83521/95256\)	\(-78175731148856964504\)	\([]\)	\(3525120\)	\(2.4961\)	\(\Gamma_0(N)\)-optimal