Cremona's table of elliptic curves

2020 = 2² · 5 · 101

Field	Data	Notes
Atkin-Lehner	2- 5- 101+	Signs for the Atkin-Lehner involutions
Class	2020b	Isogeny class
Conductor	2020	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	1010000 = 24 · 54 · 101	Discriminant
Eigenvalues	2- -2 5- -2  2 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-25,0]	[a1,a2,a3,a4,a6]
Generators	[-5:5:1]	Generators of the group modulo torsion
j	112377856/63125	j-invariant
L	2.2275747497003	L(r)(E,1)/r!
Ω	2.3957059375851	Real period
R	0.30993992414412	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8080i1 32320g1 18180b1 10100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2020b1

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	2	-2	-2	8	0	-6	4	-6	2	-12	-8	14	-6	-6	14	4	-10	12	6	-14	2

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Quadratic twists for elliptic curve 2020b1

-4	8	-3	5	-7
8080i1	32320g1	18180b1	10100b1	98980c1

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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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