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	1008g	Isogeny class
Conductor	1008	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	423263232 = 210 · 310 · 7	Discriminant
Eigenvalues	2+ 3- -2 7-  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1371,19514]	[a1,a2,a3,a4,a6]
Generators	[-5:162:1]	Generators of the group modulo torsion
j	381775972/567	j-invariant
L	2.3063814703383	L(r)(E,1)/r!
Ω	1.6757734404935	Real period
R	0.68815432164241	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	504f3 4032bh3 336b3 25200u4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008g3

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

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Quadratic twists for elliptic curve 1008g3

-4	8	-3	5	-7	-11
504f3	4032bh3	336b3	25200u4	7056v3	121968bk4

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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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