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	2	Product of Tamagawa factors cp
Δ	-17294403 = -1 · 3 · 78	Discriminant
Eigenvalues	-1 3- -2 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-34,-217]	[a1,a2,a3,a4,a6]
j	-4354703137/17294403	j-invariant
L	0.45111540538849	L(r)(E,1)/r!
Ω	0.90223081077698	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	336e6 1344a6 63a6 525b6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21a6

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 21a6

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73
336e6	1344a6	63a6	525b6	147a6	2541l6	3549c6	6069b6	7581b6	11109i6	17661a6	20181d6	28749e5	35301e5	38829f5	46389k5	58989a5	73101b5	78141h5	94269f5	105861g5	111909i5

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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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