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	530d	Isogeny class
Conductor	530	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-84800 = -1 · 26 · 52 · 53	Discriminant
Eigenvalues	2- -1 5+ -2 -4 -3 -1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,9,13]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	80062991/84800	j-invariant
L	2.2262282009992	L(r)(E,1)/r!
Ω	2.2585592113132	Real period
R	0.082140426436758	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4240c1 16960d1 4770n1 2650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 530d1

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	-4	-3	-1	-1	7	-9	0	-7	0	-6	6	-	-4	4	12	3	10	-15	9	-6	-9

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Quadratic twists for elliptic curve 530d1

-4	8	-3	5	-7	-11	13	53
4240c1	16960d1	4770n1	2650a1	25970y1	64130f1	89570l1	28090c1

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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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