Cremona's table of elliptic curves

804 = 2² · 3 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 67+	Signs for the Atkin-Lehner involutions
Class	804d	Isogeny class
Conductor	804	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-37511424 = -1 · 28 · 37 · 67	Discriminant
Eigenvalues	2- 3- -1 -3 -2 -2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,84,36]	[a1,a2,a3,a4,a6]
Generators	[12:-54:1]	Generators of the group modulo torsion
j	253012016/146529	j-invariant
L	2.3844031579331	L(r)(E,1)/r!
Ω	1.2304488171187	Real period
R	0.092277716830598	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	3216e1 12864d1 2412a1 20100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 804d1

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	-3	-2	-2	-4	-4	7	-8	3	-3	1	-11	0	11	-3	8	+	8	-9	0	11	-6	-6

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Quadratic twists for elliptic curve 804d1

-4	8	-3	5	-7	-11	-67
3216e1	12864d1	2412a1	20100b1	39396a1	97284k1	53868c1

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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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