Cremona's table of elliptic curves

3042 = 2 · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+	Signs for the Atkin-Lehner involutions
Class	3042d	Isogeny class
Conductor	3042	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	390739492089196848 = 24 · 311 · 1310	Discriminant
Eigenvalues	2+ 3-  2 -4 -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-31544811,-68185140971]	[a1,a2,a3,a4,a6]
j	986551739719628473/111045168	j-invariant
L	1.0192660461285	L(r)(E,1)/r!
Ω	0.063704127883028	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24336bs4 97344ci4 1014e4 76050ey4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042d3

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
+	-	2	-4	-4	+	-2	8	0	-6	4	2	-10	4	8	10	4	-2	16	-8	-2	8	12	14	-10

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Quadratic twists for elliptic curve 3042d3

-4	8	-3	5	13
24336bs4	97344ci4	1014e4	76050ey4	234d3

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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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