Cremona's table of elliptic curves

3535 = 5 · 7 · 101

Field	Data	Notes
Atkin-Lehner	5- 7+ 101-	Signs for the Atkin-Lehner involutions
Class	3535b	Isogeny class
Conductor	3535	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	-857241035 = -1 · 5 · 75 · 1012	Discriminant
Eigenvalues	-2 -1 5- 7+  3 -3  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,170,1066]	[a1,a2,a3,a4,a6]
Generators	[7:50:1]	Generators of the group modulo torsion
j	540148649984/857241035	j-invariant
L	1.5075593951397	L(r)(E,1)/r!
Ω	1.078133878731	Real period
R	0.69915222259509	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56560v1 31815c1 17675g1 24745c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3535b1

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	-1	-	+	3	-3	3	-2	2	5	-10	-2	-4	6	9	-6	-14	-2	-2	12	6	-9	0	-8	-1

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Quadratic twists for elliptic curve 3535b1

-4	-3	5	-7
56560v1	31815c1	17675g1	24745c1

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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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