Cremona's table of elliptic curves

10535 = 5 · 7² · 43

Field	Data	Notes
Atkin-Lehner	5+ 7- 43+	Signs for the Atkin-Lehner involutions
Class	10535a	Isogeny class
Conductor	10535	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	33600	Modular degree for the optimal curve
Δ	-9326727417875 = -1 · 53 · 79 · 432	Discriminant
Eigenvalues	0  1 5+ 7-  5 -1  5  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-164411,-25714580]	[a1,a2,a3,a4,a6]
j	-12179700416512/231125	j-invariant
L	1.8967326029565	L(r)(E,1)/r!
Ω	0.11854578768478	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	94815bd1 52675f1 10535d1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10535a1

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	1	+	-	5	-1	5	4	0	5	-2	-6	8	+	3	8	-6	-4	0	-8	-6	-13	-4	10	1

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Quadratic twists for elliptic curve 10535a1

-3	5	-7
94815bd1	52675f1	10535d1

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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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