Cremona's table of elliptic curves

639 = 3² · 71

Field	Data	Notes
Atkin-Lehner	3- 71-	Signs for the Atkin-Lehner involutions
Class	639a	Isogeny class
Conductor	639	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-465831 = -1 · 38 · 71	Discriminant
Eigenvalues	-1 3- -2  2  0 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,4,-34]	[a1,a2,a3,a4,a6]
Generators	[6:10:1]	Generators of the group modulo torsion
j	12167/639	j-invariant
L	1.3874418665602	L(r)(E,1)/r!
Ω	1.415921603984	Real period
R	0.97988607748923	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10224o1 40896w1 213a1 15975m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 639a1

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	2	0	-2	0	0	0	2	-10	-6	0	-4	-12	4	-12	10	2	-	-10	4	4	-6	-2

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Quadratic twists for elliptic curve 639a1

-4	8	-3	5	-7	-11	13	-71
10224o1	40896w1	213a1	15975m1	31311l1	77319u1	107991a1	45369a1

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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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