Cremona's table of elliptic curves

534 = 2 · 3 · 89

Field	Data	Notes
Atkin-Lehner	2- 3+ 89-	Signs for the Atkin-Lehner involutions
Class	534a	Isogeny class
Conductor	534	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-5132808 = -1 · 23 · 34 · 892	Discriminant
Eigenvalues	2- 3+ -2 -2 -4  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,26,107]	[a1,a2,a3,a4,a6]
Generators	[-1:9:1]	Generators of the group modulo torsion
j	1939096223/5132808	j-invariant
L	2.2001094029606	L(r)(E,1)/r!
Ω	1.6977294634534	Real period
R	0.43197094517939	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	4272d2 17088e2 1602a2 13350f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 534a2

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

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Quadratic twists for elliptic curve 534a2

-4	8	-3	5	-7	-11	13	89
4272d2	17088e2	1602a2	13350f2	26166w2	64614e2	90246a2	47526i2

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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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