Cremona's table of elliptic curves

2040 = 2³ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	2040a	Isogeny class
Conductor	2040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	16646400 = 28 · 32 · 52 · 172	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-76,-140]	[a1,a2,a3,a4,a6]
Generators	[-6:8:1]	Generators of the group modulo torsion
j	192143824/65025	j-invariant
L	2.4837450423787	L(r)(E,1)/r!
Ω	1.65939483023	Real period
R	1.4967776186421	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4080k2 16320bf2 6120w2 10200bi2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040a2

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
+	+	+	0	0	-2	+	4	0	10	-8	-6	-2	-8	0	2	-12	14	-8	4	6	-16	4	-6	-2

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Quadratic twists for elliptic curve 2040a2

-4	8	-3	5	-7	17
4080k2	16320bf2	6120w2	10200bi2	99960bs2	34680x2

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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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