Cremona's table of elliptic curves

3026 = 2 · 17 · 89

Field	Data	Notes
Atkin-Lehner	2- 17- 89+	Signs for the Atkin-Lehner involutions
Class	3026d	Isogeny class
Conductor	3026	Conductor
∏ cp	25	Product of Tamagawa factors cp
deg	1200	Modular degree for the optimal curve
Δ	-4043752736 = -1 · 25 · 175 · 89	Discriminant
Eigenvalues	2- -1  1 -2  2 -1 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,345,-1667]	[a1,a2,a3,a4,a6]
Generators	[3917:243232:1]	Generators of the group modulo torsion
j	4540485764879/4043752736	j-invariant
L	4.1653332622098	L(r)(E,1)/r!
Ω	0.76367645951097	Real period
R	5.4543166943723	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	24208g1 96832e1 27234c1 75650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3026d1

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	-2	2	-1	-	0	-6	0	2	-2	-3	4	-12	4	0	-8	-7	-8	-6	-5	4	+	-12

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Quadratic twists for elliptic curve 3026d1

-4	8	-3	5	17
24208g1	96832e1	27234c1	75650a1	51442e1

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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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