Cremona's table of elliptic curves

2010 = 2 · 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 67+	Signs for the Atkin-Lehner involutions
Class	2010f	Isogeny class
Conductor	2010	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-2170800000 = -1 · 27 · 34 · 55 · 67	Discriminant
Eigenvalues	2- 3+ 5- -1 -1 -6 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-80,2225]	[a1,a2,a3,a4,a6]
Generators	[3:-47:1]	Generators of the group modulo torsion
j	-56667352321/2170800000	j-invariant
L	3.7827324492119	L(r)(E,1)/r!
Ω	1.2181729862093	Real period
R	0.044360723477294	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16080z1 64320bb1 6030f1 10050k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2010f1

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
-	+	-	-1	-1	-6	-2	-2	0	-4	-8	-3	-6	10	6	12	-10	-11	+	-3	0	6	-1	-3	7

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Quadratic twists for elliptic curve 2010f1

-4	8	-3	5	-7
16080z1	64320bb1	6030f1	10050k1	98490bp1

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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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