Cremona's table of elliptic curves

2064 = 2⁴ · 3 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 43-	Signs for the Atkin-Lehner involutions
Class	2064i	Isogeny class
Conductor	2064	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-378092040192 = -1 · 212 · 33 · 434	Discriminant
Eigenvalues	2- 3+  2  0  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1688,12208]	[a1,a2,a3,a4,a6]
Generators	[218:3270:1]	Generators of the group modulo torsion
j	129784785047/92307627	j-invariant
L	2.8923271070208	L(r)(E,1)/r!
Ω	0.60417426208028	Real period
R	4.7872398553721	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	129b4 8256bm4 6192x4 51600cq3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2064i4

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

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Quadratic twists for elliptic curve 2064i4

-4	8	-3	5	-7	-43
129b4	8256bm4	6192x4	51600cq3	101136da3	88752bg3

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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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