Cremona's table of elliptic curves

35574 = 2 · 3 · 7² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	35574bs	Isogeny class
Conductor	35574	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-30305960745984 = -1 · 210 · 33 · 77 · 113	Discriminant
Eigenvalues	2- 3+  2 7- 11+  6  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3627,-279399]	[a1,a2,a3,a4,a6]
Generators	[105:662:1]	Generators of the group modulo torsion
j	-33698267/193536	j-invariant
L	8.8438784229254	L(r)(E,1)/r!
Ω	0.27577675730552	Real period
R	3.206897676706	Regulator
r	1	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	106722ce1 5082y1 35574g1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 35574bs1

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

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Quadratic twists for elliptic curve 35574bs1

-3	-7	-11
106722ce1	5082y1	35574g1

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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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