Cremona's table of elliptic curves

3604 = 2² · 17 · 53

Field	Data	Notes
Atkin-Lehner	2- 17- 53+	Signs for the Atkin-Lehner involutions
Class	3604a	Isogeny class
Conductor	3604	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	230656 = 28 · 17 · 53	Discriminant
Eigenvalues	2-  1 -1  0  2  1 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21,23]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	4194304/901	j-invariant
L	3.8642902003307	L(r)(E,1)/r!
Ω	2.9641508600769	Real period
R	0.43455842642576	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	14416i1 57664s1 32436g1 90100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3604a1

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

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Quadratic twists for elliptic curve 3604a1

-4	8	-3	5	17
14416i1	57664s1	32436g1	90100b1	61268a1

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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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