Cremona's table of elliptic curves

219 = 3 · 73

Field	Data	Notes
Atkin-Lehner	3+ 73+	Signs for the Atkin-Lehner involutions
Class	219a	Isogeny class
Conductor	219	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-219 = -1 · 3 · 73	Discriminant
Eigenvalues	-2 3+ -1  2 -4 -2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-6,8]	[a1,a2,a3,a4,a6]
Generators	[2:-1:1]	Generators of the group modulo torsion
j	-28094464/219	j-invariant
L	0.74457129518683	L(r)(E,1)/r!
Ω	5.6338346986015	Real period
R	0.13216065699827	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3504u1 14016s1 657b1 5475i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 219a1

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
-2	+	-1	2	-4	-2	-3	-1	0	-10	-6	1	2	6	7	3	1	-5	-13	10	+	-1	-11	-2	-11

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Quadratic twists for elliptic curve 219a1

-4	8	-3	5	-7	-11	13	17	-19	-23	73
3504u1	14016s1	657b1	5475i1	10731g1	26499f1	37011c1	63291m1	79059m1	115851i1	15987d1

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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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