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	12	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	24772608000 = 220 · 33 · 53 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7960,-270608]	[a1,a2,a3,a4,a6]
Generators	[-51:10:1]	Generators of the group modulo torsion
j	13619385906841/6048000	j-invariant
L	2.5723360911699	L(r)(E,1)/r!
Ω	0.50545013393832	Real period
R	1.6963995182716	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	210b1 6720bw1 5040bc1 8400cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680m1

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 1680m1

-4	8	-3	5	-7
210b1	6720bw1	5040bc1	8400cf1	11760cd1

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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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