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	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	15854469120 = 224 · 33 · 5 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-656,2496]	[a1,a2,a3,a4,a6]
j	7633736209/3870720	j-invariant
L	1.09598520644	L(r)(E,1)/r!
Ω	1.09598520644	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	210a1 6720cg1 5040bj1 8400ce1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680k1

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 1680k1

-4	8	-3	5	-7
210a1	6720cg1	5040bj1	8400ce1	11760co1

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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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