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	3042a	Isogeny class
Conductor	3042	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-19761264961776 = -1 · 24 · 39 · 137	Discriminant
Eigenvalues	2+ 3+ -2  2 -4 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4848,-249040]	[a1,a2,a3,a4,a6]
Generators	[92:232:1]	Generators of the group modulo torsion
j	-132651/208	j-invariant
L	2.3003556738829	L(r)(E,1)/r!
Ω	0.27116055319424	Real period
R	4.2416856854453	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	24336be1 97344h1 3042i1 76050dm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042a1

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 3042a1

-4	8	-3	5	13
24336be1	97344h1	3042i1	76050dm1	234b1

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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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