Cremona's table of elliptic curves

2021 = 43 · 47

Field	Data	Notes
Atkin-Lehner	43- 47+	Signs for the Atkin-Lehner involutions
Class	2021a	Isogeny class
Conductor	2021	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	400	Modular degree for the optimal curve
Δ	-94987 = -1 · 43 · 472	Discriminant
Eigenvalues	-2  0  0 -4 -3 -7 -3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-65,202]	[a1,a2,a3,a4,a6]
Generators	[4:2:1] [10:23:1]	Generators of the group modulo torsion
j	-30371328000/94987	j-invariant
L	1.830209514617	L(r)(E,1)/r!
Ω	3.3919291750999	Real period
R	0.26978887531801	Regulator
r	2	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32336g1 129344a1 18189g1 50525b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2021a1

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	0	0	-4	-3	-7	-3	-8	-3	8	5	-2	-5	-	+	-1	-4	4	7	8	2	4	-5	-12	-5

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Quadratic twists for elliptic curve 2021a1

-4	8	-3	5	-7	-43	-47
32336g1	129344a1	18189g1	50525b1	99029b1	86903g1	94987a1

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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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