Cremona's table of elliptic curves

1680 = 2⁴ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	1680k	Isogeny class
Conductor	1680	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-55566000000000000 = -1 · 213 · 34 · 512 · 73	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11664,11327040]	[a1,a2,a3,a4,a6]
j	42841933504271/13565917968750	j-invariant
L	1.09598520644	L(r)(E,1)/r!
Ω	0.27399630160999	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	210a8 6720cg8 5040bj8 8400ce8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680k8

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

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Quadratic twists for elliptic curve 1680k8

-4	8	-3	5	-7
210a8	6720cg8	5040bj8	8400ce8	11760co8

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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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