Cremona's table of elliptic curves

20 = 2² · 5

Field	Data	Notes
Atkin-Lehner	2- 5+	Signs for the Atkin-Lehner involutions
Class	20a	Isogeny class
Conductor	20	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1	Modular degree for the optimal curve
Δ	-6400 = -1 · 28 · 52	Discriminant
Eigenvalues	2- -2 5+  2  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,4,4]	[a1,a2,a3,a4,a6]
j	21296/25	j-invariant
L	0.47072919032652	L(r)(E,1)/r!
Ω	2.8243751419591	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	80b1 320c2 180a2 100a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20a1

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 20a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79
80b1	320c2	180a2	100a2	980g2	2420e2	3380i2	5780e2	7220c2	10580m2	16820b2	19220b2	27380d2	33620a2	36980a2	44180g2	56180d2	69620b2	74420d2	89780f2	100820a2	106580d2	124820b2

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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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