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	3026b	Isogeny class
Conductor	3026	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	400	Modular degree for the optimal curve
Δ	-48416 = -1 · 25 · 17 · 89	Discriminant
Eigenvalues	2-  1  1 -4  4 -5 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-45,113]	[a1,a2,a3,a4,a6]
Generators	[4:-1:1]	Generators of the group modulo torsion
j	-10091699281/48416	j-invariant
L	5.3001478069031	L(r)(E,1)/r!
Ω	3.5926218458573	Real period
R	0.29505737226503	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	24208e1 96832b1 27234f1 75650j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3026b1

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	-4	4	-5	+	-4	-2	-4	-4	8	-11	-6	8	6	6	10	3	-8	0	-11	-8	-	4

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Quadratic twists for elliptic curve 3026b1

-4	8	-3	5	17
24208e1	96832b1	27234f1	75650j1	51442h1

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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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