Cremona's table of elliptic curves

285 = 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	285b	Isogeny class
Conductor	285	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-135375 = -1 · 3 · 53 · 192	Discriminant
Eigenvalues	1 3+ 5+ -2 -2 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,2,-17]	[a1,a2,a3,a4,a6]
Generators	[6:13:1]	Generators of the group modulo torsion
j	357911/135375	j-invariant
L	1.6159662807376	L(r)(E,1)/r!
Ω	1.5380021358662	Real period
R	2.1013836626792	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4560y1 18240bq1 855b1 1425g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 285b1

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	+	+	-2	-2	-4	2	+	-4	4	0	0	0	-10	12	-2	4	2	-16	0	-2	-8	-12	0	-16

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Quadratic twists for elliptic curve 285b1

-4	8	-3	5	-7	-11	13	17	-19
4560y1	18240bq1	855b1	1425g1	13965x1	34485c1	48165k1	82365m1	5415h1

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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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