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	285a	Isogeny class
Conductor	285	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-438615 = -1 · 35 · 5 · 192	Discriminant
Eigenvalues	-1 3- 5+ -2 -6  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,19,0]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	756058031/438615	j-invariant
L	1.1896124822811	L(r)(E,1)/r!
Ω	1.7646479000603	Real period
R	0.26965435591779	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	4560k1 18240t1 855c1 1425c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 285a1

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	-6	0	-6	-	-8	4	0	4	0	-2	-8	2	12	2	-8	16	14	8	0	0	-12

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Quadratic twists for elliptic curve 285a1

-4	8	-3	5	-7	-11	13	17	-19
4560k1	18240t1	855c1	1425c1	13965l1	34485m1	48165y1	82365f1	5415c1

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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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