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	804a	Isogeny class
Conductor	804	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	1012808448 = 28 · 310 · 67	Discriminant
Eigenvalues	2- 3+  4  0  0  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-276,-792]	[a1,a2,a3,a4,a6]
j	9115564624/3956283	j-invariant
L	1.8272941754665	L(r)(E,1)/r!
Ω	1.2181961169777	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	3216m2 12864w2 2412c2 20100i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 804a2

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
-	+	4	0	0	2	2	4	-6	-6	0	-6	12	-4	10	12	6	6	+	-2	2	0	-6	10	-18

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Quadratic twists for elliptic curve 804a2

-4	8	-3	5	-7	-11	-67
3216m2	12864w2	2412c2	20100i2	39396m2	97284d2	53868j2

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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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