Cremona's table of elliptic curves

63 = 3² · 7

Field	Data	Notes
Atkin-Lehner	3- 7+	Signs for the Atkin-Lehner involutions
Class	63a	Isogeny class
Conductor	63	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	15752961 = 38 · 74	Discriminant
Eigenvalues	1 3-  2 7+ -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-441,3672]	[a1,a2,a3,a4,a6]
j	13027640977/21609	j-invariant
L	1.1033104643357	L(r)(E,1)/r!
Ω	2.2066209286714	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	1008k3 4032h4 21a2 1575g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 63a4

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 63a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
1008k3	4032h4	21a2	1575g4	441c3	7623p3	10647f4	18207e4	22743n4	33327m4	52983a4	60543g4	86247g4	105903i4	116487m4

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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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