Elliptic curve isogeny class with Cremona label 85063a (LMFDB label 85063.b)

• Label: 85063a
• Number of curves: $1$
• Conductor: $85063$
• CM: no
• Rank: $0$

Rank

The elliptic curve 85063a1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11\)	\(1\)
\(19\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 85063a do not have complex multiplication.

Modular form 85063.2.a.a

Elliptic curves in class 85063a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
85063.b1	85063a1	\([0, 0, 1, -461978, 88370081]\)	\(6155048569503744/1657637226773\)	\(2936605463099202653\)	\([]\)	\(1123200\)	\(2.2518\)	\(\Gamma_0(N)\)-optimal