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	147 = 3 · 72	Discriminant
Eigenvalues	-1 3- -2 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-784,-8515]	[a1,a2,a3,a4,a6]
j	53297461115137/147	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	336e5 1344a5 63a5 525b5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21a5

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 21a5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73
336e5	1344a5	63a5	525b5	147a5	2541l5	3549c5	6069b5	7581b5	11109i5	17661a5	20181d5	28749e6	35301e6	38829f6	46389k6	58989a6	73101b6	78141h6	94269f6	105861g6	111909i6

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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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