Cremona's table of elliptic curves

3082 = 2 · 23 · 67

Field	Data	Notes
Atkin-Lehner	2- 23- 67+	Signs for the Atkin-Lehner involutions
Class	3082a	Isogeny class
Conductor	3082	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	832	Modular degree for the optimal curve
Δ	-394496 = -1 · 28 · 23 · 67	Discriminant
Eigenvalues	2- -3  1  4 -2 -2 -6 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,18,-3]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	679151439/394496	j-invariant
L	3.5801953383143	L(r)(E,1)/r!
Ω	1.8065161989817	Real period
R	0.24772787398284	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	24656e1 98624i1 27738e1 77050e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3082a1

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	1	4	-2	-2	-6	-3	-	-6	-7	10	-12	4	-4	3	0	6	+	-12	-2	-2	9	0	-11

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Quadratic twists for elliptic curve 3082a1

-4	8	-3	5	-23
24656e1	98624i1	27738e1	77050e1	70886g1

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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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