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	3042i	Isogeny class
Conductor	3042	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	88098917868 = 22 · 33 · 138	Discriminant
Eigenvalues	2- 3+  2  2  4 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10679,427171]	[a1,a2,a3,a4,a6]
j	1033364331/676	j-invariant
L	4.2575438006316	L(r)(E,1)/r!
Ω	1.0643859501579	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24336bd2 97344p2 3042a2 76050i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042i2

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

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Quadratic twists for elliptic curve 3042i2

-4	8	-3	5	13
24336bd2	97344p2	3042a2	76050i2	234c2

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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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