Cremona's table of elliptic curves

20535 = 3 · 5 · 37²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 37+	Signs for the Atkin-Lehner involutions
Class	20535a	Isogeny class
Conductor	20535	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	129889899455625 = 34 · 54 · 376	Discriminant
Eigenvalues	1 3+ 5+  0 -4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13718,-291753]	[a1,a2,a3,a4,a6]
Generators	[-61690:600491:1000]	Generators of the group modulo torsion
j	111284641/50625	j-invariant
L	3.8369157426523	L(r)(E,1)/r!
Ω	0.46051544355256	Real period
R	8.3317851689252	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	61605k3 102675s3 15a1	Quadratic twists by: -3 5 37

Hecke Eigenvalues for elliptic curve 20535a3

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
1	+	+	0	-4	2	-2	-4	0	2	0	+	10	-4	8	-10	4	2	12	-8	10	0	12	6	-2

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Quadratic twists for elliptic curve 20535a3

-3	5	37
61605k3	102675s3	15a1

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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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