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	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	4240 = 24 · 5 · 53	Discriminant
Eigenvalues	2+  0 5- -2  0 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4,0]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	8120601/4240	j-invariant
L	1.5252750504437	L(r)(E,1)/r!
Ω	3.5353430676396	Real period
R	0.86287244053071	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	4240f1 16960a1 4770y1 2650f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 530b1

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 530b1

-4	8	-3	5	-7	-11	13	53
4240f1	16960a1	4770y1	2650f1	25970g1	64130s1	89570r1	28090d1

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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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