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	1680m	Isogeny class
Conductor	1680	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	353561707806720 = 236 · 3 · 5 · 73	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-23560,1065712]	[a1,a2,a3,a4,a6]
Generators	[-3:1066:1]	Generators of the group modulo torsion
j	353108405631241/86318776320	j-invariant
L	2.5723360911699	L(r)(E,1)/r!
Ω	0.50545013393832	Real period
R	5.0891985548148	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	210b3 6720bw3 5040bc3 8400cf3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680m3

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

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Quadratic twists for elliptic curve 1680m3

-4	8	-3	5	-7
210b3	6720bw3	5040bc3	8400cf3	11760cd3

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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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