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	1825955703416823732 = 22 · 316 · 139	Discriminant
Eigenvalues	2+ 3- -2  2  0 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-321723,26662689]	[a1,a2,a3,a4,a6]
Generators	[-462:8979:1]	Generators of the group modulo torsion
j	476379541/236196	j-invariant
L	2.3550616847308	L(r)(E,1)/r!
Ω	0.2341682383906	Real period
R	2.5142838551855	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	24336ce2 97344dc2 1014g2 76050fi2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042g2

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 3042g2

-4	8	-3	5	13
24336ce2	97344dc2	1014g2	76050fi2	3042n2

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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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