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	2010b	Isogeny class
Conductor	2010	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	404010 = 2 · 32 · 5 · 672	Discriminant
Eigenvalues	2+ 3+ 5-  2  0  2 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-57,-189]	[a1,a2,a3,a4,a6]
Generators	[-5:4:1]	Generators of the group modulo torsion
j	21047437081/404010	j-invariant
L	2.1799194781167	L(r)(E,1)/r!
Ω	1.7355999773536	Real period
R	1.2560034031809	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	16080w2 64320x2 6030v2 10050bh2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2010b2

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

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Quadratic twists for elliptic curve 2010b2

-4	8	-3	5	-7
16080w2	64320x2	6030v2	10050bh2	98490t2

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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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