Cremona's table of elliptic curves

3894 = 2 · 3 · 11 · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 59+	Signs for the Atkin-Lehner involutions
Class	3894o	Isogeny class
Conductor	3894	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-8971776 = -1 · 29 · 33 · 11 · 59	Discriminant
Eigenvalues	2- 3- -3  2 11+ -4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12,144]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	-192100033/8971776	j-invariant
L	5.3705286700004	L(r)(E,1)/r!
Ω	1.9191277977264	Real period
R	0.93280719786055	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	31152u1 124608w1 11682l1 97350e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3894o1

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	2	+	-4	-3	-1	0	-6	-4	5	-6	8	-3	-3	+	-10	-4	0	-7	8	-9	-15	-10

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Quadratic twists for elliptic curve 3894o1

-4	8	-3	5	-11
31152u1	124608w1	11682l1	97350e1	42834s1

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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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