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	1680p	Isogeny class
Conductor	1680	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	4978713600000000 = 216 · 34 · 58 · 74	Discriminant
Eigenvalues	2- 3+ 5- 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-120800,15840000]	[a1,a2,a3,a4,a6]
j	47595748626367201/1215506250000	j-invariant
L	1.723611497434	L(r)(E,1)/r!
Ω	0.43090287435849	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	210e3 6720cd4 5040bi3 8400cc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680p4

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
-	+	-	-	4	-2	2	-4	8	-2	0	6	-6	4	0	-10	-12	14	12	8	10	-16	12	10	2

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Quadratic twists for elliptic curve 1680p4

-4	8	-3	5	-7
210e3	6720cd4	5040bi3	8400cc4	11760ch3

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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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