Cremona's table of elliptic curves

1008 = 2⁴ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7+	Signs for the Atkin-Lehner involutions
Class	1008j	Isogeny class
Conductor	1008	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-15431472 = -1 · 24 · 39 · 72	Discriminant
Eigenvalues	2- 3-  0 7+ -6  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,60,-61]	[a1,a2,a3,a4,a6]
Generators	[13:54:1]	Generators of the group modulo torsion
j	2048000/1323	j-invariant
L	2.3940039827047	L(r)(E,1)/r!
Ω	1.2645801725874	Real period
R	0.94656077748176	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	252a1 4032bb1 336a1 25200eu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008j1

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

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Quadratic twists for elliptic curve 1008j1

-4	8	-3	5	-7	-11
252a1	4032bb1	336a1	25200eu1	7056br1	121968fk1

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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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