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	35574h	Isogeny class
Conductor	35574	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	47520	Modular degree for the optimal curve
Δ	-1134387198252 = -1 · 22 · 33 · 72 · 118	Discriminant
Eigenvalues	2+ 3+  0 7- 11-  1  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-970,52144]	[a1,a2,a3,a4,a6]
Generators	[50:338:1]	Generators of the group modulo torsion
j	-9625/108	j-invariant
L	3.4966065732035	L(r)(E,1)/r!
Ω	0.73929628006897	Real period
R	0.78827362981751	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	106722gf1 35574s1 35574bv1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 35574h1

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	0	4	6	0	-5	-7	-6	-7	6	12	0	7	8	-12	7	8	-6	-12	7

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Quadratic twists for elliptic curve 35574h1

-3	-7	-11
106722gf1	35574s1	35574bv1

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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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