Cremona's table of elliptic curves

530 = 2 · 5 · 53

Field	Data	Notes
Atkin-Lehner	2+ 5- 53-	Signs for the Atkin-Lehner involutions
Class	530b	Isogeny class
Conductor	530	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-280900 = -1 · 22 · 52 · 532	Discriminant
Eigenvalues	2+  0 5- -2  0 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,16,-12]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	437245479/280900	j-invariant
L	1.5252750504437	L(r)(E,1)/r!
Ω	1.7676715338198	Real period
R	0.43143622026535	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	4240f2 16960a2 4770y2 2650f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 530b2

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
+	0	-	-2	0	-2	-6	-2	0	2	-2	-2	10	-10	-6	-	-12	-2	-16	-6	10	10	8	14	-6

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Quadratic twists for elliptic curve 530b2

-4	8	-3	5	-7	-11	13	53
4240f2	16960a2	4770y2	2650f2	25970g2	64130s2	89570r2	28090d2

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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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