Cremona's table of elliptic curves

21 = 3 · 7

Field	Data	Notes
Atkin-Lehner	3- 7+	Signs for the Atkin-Lehner involutions
Class	21a	Isogeny class
Conductor	21	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	45927 = 38 · 7	Discriminant
Eigenvalues	-1 3- -2 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-39,90]	[a1,a2,a3,a4,a6]
j	6570725617/45927	j-invariant
L	0.45111540538849	L(r)(E,1)/r!
Ω	3.6089232431079	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	336e3 1344a4 63a3 525b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21a3

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
-1	-	-2	+	4	-2	-6	4	0	-2	0	6	2	-4	0	6	12	-2	4	0	-6	-16	-12	-14	18

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Quadratic twists for elliptic curve 21a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73
336e3	1344a4	63a3	525b4	147a3	2541l3	3549c4	6069b4	7581b3	11109i3	17661a4	20181d3	28749e3	35301e3	38829f3	46389k3	58989a3	73101b3	78141h3	94269f3	105861g3	111909i3

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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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