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	4	Product of Tamagawa factors cp
Δ	-12607619787 = -1 · 37 · 78	Discriminant
Eigenvalues	1 3-  2 7+ -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-306,5859]	[a1,a2,a3,a4,a6]
j	-4354703137/17294403	j-invariant
L	1.1033104643357	L(r)(E,1)/r!
Ω	1.1033104643357	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	1008k6 4032h6 21a6 1575g6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 63a6

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 63a6

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
1008k6	4032h6	21a6	1575g6	441c6	7623p6	10647f6	18207e6	22743n5	33327m5	52983a5	60543g5	86247g5	105903i5	116487m5

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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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