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	4	Product of Tamagawa factors cp
Δ	2671875 = 32 · 56 · 19	Discriminant
Eigenvalues	1 3+ 5+ -2 -2 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-93,-378]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	90458382169/2671875	j-invariant
L	1.6159662807376	L(r)(E,1)/r!
Ω	1.5380021358662	Real period
R	1.0506918313396	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	4560y2 18240bq2 855b2 1425g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 285b2

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 285b2

-4	8	-3	5	-7	-11	13	17	-19
4560y2	18240bq2	855b2	1425g2	13965x2	34485c2	48165k2	82365m2	5415h2

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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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