Cremona's table of elliptic curves

3059 = 7 · 19 · 23

Field	Data	Notes
Atkin-Lehner	7- 19- 23+	Signs for the Atkin-Lehner involutions
Class	3059b	Isogeny class
Conductor	3059	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	77695164743 = 72 · 194 · 233	Discriminant
Eigenvalues	-1  2  0 7-  4 -6 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-64838,-6381668]	[a1,a2,a3,a4,a6]
Generators	[8094:25931:27]	Generators of the group modulo torsion
j	30144838467846390625/77695164743	j-invariant
L	3.063049725	L(r)(E,1)/r!
Ω	0.29918663170922	Real period
R	5.1189615450081	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48944o2 27531d2 76475f2 21413a2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3059b2

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	2	0	-	4	-6	-4	-	+	-6	6	-2	2	-4	-2	-6	-10	4	-4	4	-2	0	0	-8	4

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Quadratic twists for elliptic curve 3059b2

-4	-3	5	-7	-19	-23
48944o2	27531d2	76475f2	21413a2	58121c2	70357a2

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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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