Cremona's table of elliptic curves

1764 = 2² · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	1764f	Isogeny class
Conductor	1764	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-484334321737392 = -1 · 24 · 37 · 712	Discriminant
Eigenvalues	2- 3-  0 7-  6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-49980,-4429159]	[a1,a2,a3,a4,a6]
j	-10061824000/352947	j-invariant
L	1.9118655140397	L(r)(E,1)/r!
Ω	0.15932212616997	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7056br3 28224bo3 588b3 44100cn3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1764f3

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

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Quadratic twists for elliptic curve 1764f3

-4	8	-3	5	-7
7056br3	28224bo3	588b3	44100cn3	252a3

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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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