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	8	Product of Tamagawa factors cp
deg	3328	Modular degree for the optimal curve
Δ	339443776 = 26 · 74 · 472	Discriminant
Eigenvalues	2-  0  2 7+ -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-769,-8160]	[a1,a2,a3,a4,a6]
Generators	[631329:6973920:4913]	Generators of the group modulo torsion
j	785819420352/5303809	j-invariant
L	4.6677829220335	L(r)(E,1)/r!
Ω	0.90697350332537	Real period
R	10.293096556667	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10528f1 21056n2 94752c1 73696i1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10528d1

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 10528d1

-4	8	-3	-7
10528f1	21056n2	94752c1	73696i1

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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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