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	804c	Isogeny class
Conductor	804	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-51456 = -1 · 28 · 3 · 67	Discriminant
Eigenvalues	2- 3+ -3  3 -2  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12,24]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	-810448/201	j-invariant
L	1.8789758549497	L(r)(E,1)/r!
Ω	3.3871101427219	Real period
R	0.18491435429966	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	3216h1 12864o1 2412e1 20100h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 804c1

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
-	+	-3	3	-2	2	0	-4	-5	-4	5	-11	-5	-5	-8	1	9	-12	-	0	-9	0	-1	14	-6

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Quadratic twists for elliptic curve 804c1

-4	8	-3	5	-7	-11	-67
3216h1	12864o1	2412e1	20100h1	39396r1	97284h1	53868i1

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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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