Cremona's table of elliptic curves

30528 = 2⁶ · 3² · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 53+	Signs for the Atkin-Lehner involutions
Class	30528bk	Isogeny class
Conductor	30528	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-7283414466035712 = -1 · 226 · 36 · 533	Discriminant
Eigenvalues	2- 3-  0  4  0 -5  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14171340,-20533571696]	[a1,a2,a3,a4,a6]
Generators	[413229423747072258868243758:-192300659108104701458147837440:1907568396044352157823]	Generators of the group modulo torsion
j	-1646982616152408625/38112512	j-invariant
L	6.457920381848	L(r)(E,1)/r!
Ω	0.038906022083261	Real period
R	41.496920245584	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	30528g2 7632m2 3392p2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 30528bk2

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	4	0	-5	3	-1	3	9	4	-5	-6	-10	6	+	-6	-8	-4	-3	-4	13	-3	-18	-7

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Quadratic twists for elliptic curve 30528bk2

-4	8	-3
30528g2	7632m2	3392p2

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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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