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	16	Product of Tamagawa factors cp
Δ	64224111125772 = 22 · 39 · 138	Discriminant
Eigenvalues	2+ 3+ -2  2 -4 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-96108,-11437516]	[a1,a2,a3,a4,a6]
Generators	[-182:118:1]	Generators of the group modulo torsion
j	1033364331/676	j-invariant
L	2.3003556738829	L(r)(E,1)/r!
Ω	0.27116055319424	Real period
R	2.1208428427226	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	24336be2 97344h2 3042i2 76050dm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042a2

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 3042a2

-4	8	-3	5	13
24336be2	97344h2	3042i2	76050dm2	234b2

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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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