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	3042k	Isogeny class
Conductor	3042	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	4704	Modular degree for the optimal curve
Δ	-5855189618304 = -1 · 27 · 36 · 137	Discriminant
Eigenvalues	2- 3- -1 -1 -2 13+  3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4088,-152837]	[a1,a2,a3,a4,a6]
Generators	[101:625:1]	Generators of the group modulo torsion
j	-2146689/1664	j-invariant
L	4.5111433395717	L(r)(E,1)/r!
Ω	0.28888034773498	Real period
R	0.55771278105552	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24336bl1 97344bc1 338f1 76050bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042k1

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
-	-	-1	-1	-2	+	3	-6	4	-2	-4	-3	0	-5	13	-12	-10	-8	2	-5	10	-4	0	6	-14

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Quadratic twists for elliptic curve 3042k1

-4	8	-3	5	13
24336bl1	97344bc1	338f1	76050bd1	234a1

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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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