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	530c	Isogeny class
Conductor	530	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	1200	Modular degree for the optimal curve
Δ	-530000000000 = -1 · 210 · 510 · 53	Discriminant
Eigenvalues	2+ -3 5- -2  0  1  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1226,30580]	[a1,a2,a3,a4,a6]
Generators	[156:1922:1]	Generators of the group modulo torsion
j	203702260843719/530000000000	j-invariant
L	1.0573504269566	L(r)(E,1)/r!
Ω	0.64816925965994	Real period
R	0.081564376217972	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	4240g1 16960c1 4770x1 2650j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 530c1

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
+	-3	-	-2	0	1	3	1	-3	-1	-8	-11	-8	2	-6	-	12	-8	-4	-3	-2	-17	11	2	3

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Quadratic twists for elliptic curve 530c1

-4	8	-3	5	-7	-11	13	53
4240g1	16960c1	4770x1	2650j1	25970j1	64130t1	89570w1	28090e1

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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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