Cremona's table of elliptic curves

10528 = 2⁵ · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 7+ 47-	Signs for the Atkin-Lehner involutions
Class	10528d	Isogeny class
Conductor	10528	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-138724171264 = -1 · 29 · 78 · 47	Discriminant
Eigenvalues	2-  0  2 7+ -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-299,-18030]	[a1,a2,a3,a4,a6]
Generators	[774382843142610:-5077634741876592:14198858138375]	Generators of the group modulo torsion
j	-5773874184/270945647	j-invariant
L	4.6677829220335	L(r)(E,1)/r!
Ω	0.45348675166269	Real period
R	20.586193113335	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	10528f4 21056n3 94752c2 73696i2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10528d4

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

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Quadratic twists for elliptic curve 10528d4

-4	8	-3	-7
10528f4	21056n3	94752c2	73696i2

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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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