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	3042g	Isogeny class
Conductor	3042	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	71245947275523072 = 210 · 38 · 139	Discriminant
Eigenvalues	2+ 3- -2  2  0 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-107985708,-431887255344]	[a1,a2,a3,a4,a6]
Generators	[-311333112552:155192927028:51895117]	Generators of the group modulo torsion
j	18013780041269221/9216	j-invariant
L	2.3550616847308	L(r)(E,1)/r!
Ω	0.04683364767812	Real period
R	12.571419275928	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	24336ce4 97344dc4 1014g4 76050fi4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042g4

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	0	-	-2	-6	4	10	10	-8	-10	-4	-12	6	4	2	-2	0	4	0	4	-6	-12

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Quadratic twists for elliptic curve 3042g4

-4	8	-3	5	13
24336ce4	97344dc4	1014g4	76050fi4	3042n4

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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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