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	35574v	Isogeny class
Conductor	35574	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	270588935232 = 26 · 33 · 76 · 113	Discriminant
Eigenvalues	2+ 3-  0 7- 11+  6 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1741,12296]	[a1,a2,a3,a4,a6]
Generators	[4:71:1]	Generators of the group modulo torsion
j	3723875/1728	j-invariant
L	5.5152700034733	L(r)(E,1)/r!
Ω	0.87589591059663	Real period
R	1.0494530869762	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	106722fw1 726a1 35574cq1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 35574v1

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

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Quadratic twists for elliptic curve 35574v1

-3	-7	-11
106722fw1	726a1	35574cq1

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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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