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
deg	1	Modular degree for the optimal curve
Δ	3969 = 34 · 72	Discriminant
Eigenvalues	-1 3- -2 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4,-1]	[a1,a2,a3,a4,a6]
j	7189057/3969	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	336e2 1344a2 63a2 525b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21a1

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 21a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73
336e2	1344a2	63a2	525b2	147a2	2541l2	3549c2	6069b2	7581b2	11109i2	17661a2	20181d2	28749e2	35301e2	38829f2	46389k2	58989a2	73101b2	78141h2	94269f2	105861g2	111909i2

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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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