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
deg	2688	Modular degree for the optimal curve
Δ	-27107359344 = -1 · 24 · 33 · 137	Discriminant
Eigenvalues	2- 3+  2  2  4 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-539,9403]	[a1,a2,a3,a4,a6]
j	-132651/208	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	24336bd1 97344p1 3042a1 76050i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042i1

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 3042i1

-4	8	-3	5	13
24336bd1	97344p1	3042a1	76050i1	234c1

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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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