Cremona's table of elliptic curves

3819 = 3 · 19 · 67

Field	Data	Notes
Atkin-Lehner	3+ 19+ 67-	Signs for the Atkin-Lehner involutions
Class	3819b	Isogeny class
Conductor	3819	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-767619 = -1 · 32 · 19 · 672	Discriminant
Eigenvalues	0 3+ -1 -3 -5  0  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1,-42]	[a1,a2,a3,a4,a6]
Generators	[4:1:1] [22:100:1]	Generators of the group modulo torsion
j	-262144/767619	j-invariant
L	3.0929814015016	L(r)(E,1)/r!
Ω	1.2871547100563	Real period
R	0.60074002319552	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	61104t1 11457b1 95475f1 72561h1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3819b1

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
0	+	-1	-3	-5	0	3	+	-8	-4	-8	-10	0	-7	-9	-6	4	-7	-	8	9	14	-12	-14	-14

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Quadratic twists for elliptic curve 3819b1

-4	-3	5	-19
61104t1	11457b1	95475f1	72561h1

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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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