Cremona's table of elliptic curves

21024 = 2⁵ · 3² · 73

Field	Data	Notes
Atkin-Lehner	2- 3- 73+	Signs for the Atkin-Lehner involutions
Class	21024k	Isogeny class
Conductor	21024	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	429632335872 = 212 · 39 · 732	Discriminant
Eigenvalues	2- 3- -4  2  0  6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2172,-22880]	[a1,a2,a3,a4,a6]
Generators	[-34:108:1]	Generators of the group modulo torsion
j	379503424/143883	j-invariant
L	4.4244668771189	L(r)(E,1)/r!
Ω	0.72196147913083	Real period
R	0.76604967941736	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	21024d2 42048m1 7008e2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21024k2

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
-	-	-4	2	0	6	4	-4	0	0	-2	6	2	-10	-12	-4	0	2	-8	-8	+	4	4	-2	14

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Quadratic twists for elliptic curve 21024k2

-4	8	-3
21024d2	42048m1	7008e2

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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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