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	1008c	Isogeny class
Conductor	1008	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-15431472 = -1 · 24 · 39 · 72	Discriminant
Eigenvalues	2+ 3+  2 7- -2  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-54,243]	[a1,a2,a3,a4,a6]
j	-55296/49	j-invariant
L	2.0212683374756	L(r)(E,1)/r!
Ω	2.0212683374756	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	504d1 4032y1 1008d1 25200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008c1

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	2	6	4	-6	0	4	10	2	4	-4	-12	-12	6	4	14	-2	8	16	-6	-18

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Quadratic twists for elliptic curve 1008c1

-4	8	-3	5	-7	-11
504d1	4032y1	1008d1	25200e1	7056i1	121968g1

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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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