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	4	Product of Tamagawa factors cp
Δ	21609 = 32 · 74	Discriminant
Eigenvalues	-1 3- -2 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-49,-136]	[a1,a2,a3,a4,a6]
j	13027640977/21609	j-invariant
L	0.45111540538849	L(r)(E,1)/r!
Ω	1.804461621554	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	336e4 1344a3 63a4 525b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21a2

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 21a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73
336e4	1344a3	63a4	525b3	147a4	2541l4	3549c3	6069b3	7581b4	11109i4	17661a3	20181d4	28749e4	35301e4	38829f4	46389k4	58989a4	73101b4	78141h4	94269f4	105861g4	111909i4

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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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