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	3042m	Isogeny class
Conductor	3042	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	39936	Modular degree for the optimal curve
Δ	-110979264025334016 = -1 · 28 · 312 · 138	Discriminant
Eigenvalues	2- 3- -3  2 -6 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-94334,-19502323]	[a1,a2,a3,a4,a6]
Generators	[465:5851:1]	Generators of the group modulo torsion
j	-156116857/186624	j-invariant
L	4.284459823501	L(r)(E,1)/r!
Ω	0.13024616303723	Real period
R	0.68531446589148	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	24336bz1 97344cm1 1014b1 76050bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042m1

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
-	-	-3	2	-6	+	3	2	6	-3	-4	-7	3	-10	-6	-3	0	-7	-10	-6	-13	-4	6	-18	14

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Quadratic twists for elliptic curve 3042m1

-4	8	-3	5	13
24336bz1	97344cm1	1014b1	76050bo1	3042e1

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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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