Cremona's table of elliptic curves

80 = 2⁴ · 5

Field	Data	Notes
Atkin-Lehner	2- 5+	Signs for the Atkin-Lehner involutions
Class	80b	Isogeny class
Conductor	80	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-4000000 = -1 · 28 · 56	Discriminant
Eigenvalues	2-  2 5+ -2  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-36,140]	[a1,a2,a3,a4,a6]
j	-20720464/15625	j-invariant
L	1.1370825995205	L(r)(E,1)/r!
Ω	2.2741651990411	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20a3 320f4 720i4 400e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 80b3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	2	+	-2	0	2	-6	4	-6	6	4	2	6	10	6	-6	-12	2	-2	12	2	-8	-6	-6	2

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Quadratic twists for elliptic curve 80b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
20a3	320f4	720i4	400e4	3920bf4	9680t4	13520bb4	23120bj4	28880y4	42320z4	67280q4	76880s4	109520y4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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